Math and Vocabulary for Civil Service Exams

Math and Vocabulary for Civil Service Exams

®

NEW

YORK

Copyright © 2008 LearningExpress, LLC. All rights reserved under International and Pan-American Copyright Conventions. Published in the United States by LearningExpress, LLC, New York. Library of Congress Cataloging-in-Publication Data: Math and vocabulary for civil service exams. p. cm. ISBN 978-1-57685-606-2 1. Civil service—United States—Examinations—Study guides. 2. Mathematics—Examinations—Study guides. 3. English language—Examinations—Study guides. JK716.M24 2008 513.076—dc22 2007037804 Printed in the United States of America 987654321 ISBN: 978-1-57685-606-2 For information on LearningExpress, other LearningExpress products, or bulk sales, please write to us at: LearningExpress 55 Broadway 8th Floor New York, NY 10006 Or visit us at: www.learnatest.com

Contents

SECTION 1

SECTION 2

Preparing for Your Civil Service Exam

1

CHAPTER

1

Civil Service Jobs

3

CHAPTER

2

The LearningExpress Test Preparation System

7

Math Prep for Civil Service Exams

27

CHAPTER

3

Arithmetic, Powers, and Roots

29

CHAPTER

4

Fractions and Decimals

41

CHAPTER

5

Percents

63

CHAPTER

6

Number Series

77

CHAPTER

7

Word Problems

89

CHAPTER

8

Charts, Tables, and Graphs

103

CHAPTER

9

Measurement and Geometry

125

iii

–MATH AND VOCABULARY FOR CIVIL SER VICE EXAMS–

SECTION 3

SECTION 4

SECTION 5

Vocabulary Prep for Civil Service Exams

141

CHAPTER 10

Vocabulary in Context

143

CHAPTER 11

Synonyms and Antonyms

149

CHAPTER 12

Reading Comprehension

159

CHAPTER 13

Grammar

177

CHAPTER 14

Spelling

197

Test Time!

211

CHAPTER 15

Practice Test 1

213

CHAPTER 16

Practice Test 2

233

Helpful Resources

253

APPENDIX 1

Glossary of Math Terms

255

APPENDIX 2

Math Formula Sheet

257

APPENDIX 3

Glossary of Vocabulary Terms

259

APPENDIX 4

Commonly Tested Vocabulary Words

263

APPENDIX 5

Prefixes, Suffixes, and Word Roots

289

iv

S E C T I O N

1

Preparing for Your Civil Service Exam

C

hoosing a career as a government employee can be very rewarding— you’ll see respectable salaries, generous benefit packages, and opportunities for significant career advancement. But before you begin your job, you’ll probably need to take a civil service exam. This exam requires candidates to score well on all parts of the exam, but the questions that require indepth math and vocabulary knowledge can be especially nerve-racking if it’s been a while since you’ve used these skills. Arm yourself with this book that will help you dust off your skills as you work your way through the most commonly tested math and vocabulary topics. By making the commitment to practice these difficult questions for the civil service exam, you are promising yourself increased scores and marketability as you enter this career path. Is your civil service exam months away, or even maybe a few short weeks away? Have no fear—this book will help you prepare for success by working to review and improve your math and vocabulary skills. Carefully read Chapter 1 to learn about the civil service field. Then, continue on to Chapter 2 (the LearningExpress Test Preparation System), so you can grasp effective test strategies and learn to budget your preparation time wisely. Chapter 2 presents a 30-day study plan and a 14-day study plan. You can decide which of these plans is right for you, or you can create a more personalized plan. Remember to stick as closely as you can to your study plan for the most effective results.

1

–PREPARING FOR YOUR CIVIL SER VICE EXAM–

Section 4 (“Test Time!”) includes two practice tests to help you gauge your math and vocabulary skills. These tests will give you the chance to measure what you have learned and review any problem areas you encounter. You may want to take one practice test before you begin Sections 2 and 3 to determine your areas of weakness. Then, you can take the other test after you’ve reviewed the math and vocabulary topics. Finally, don’t forget about Section 5—the resources at the end of this book. These resources include math words to know, basic math formulas, commonly tested vocabulary terms, and a list of general suffixes, prefixes, and root words. You may consult these resources at any point as you work through this book. One good use of these resources may be to make flashcards or notes about any words or formulas that are new or confusing to you. Then, work with a friend or family member to quiz yourself. You don’t even need a partner—try pulling out your flashcards as you wait in line, commute on a bus, or whenever you have a few free minutes. Always keep your end goal in mind. If you study hard the first time, you will not have to take the civil service exam again—ever! Use this book to get a feel for the math and vocabulary topics presented on the exam. Spend some quality time with these topics, take the practice tests, and then get ready to walk into the exam room with plenty of self-confidence!

Once you’ve set a study plan for yourself, look at the table of contents to see the types of math and vocabulary topics covered in this book. The book is organized in five sections: Section 1—Preparing for Your Civil Service Exam Section 2—Math Prep for Civil Service Exams Section 3—Vocabulary Prep for Civil Service Exams Section 4—Test Time! Section 5—Helpful Resources Sections 2 and 3 divide math and vocabulary concepts into compact parts so that you can work on each concept on its own and gain mastery. You may want to read the chapters in sequence, or you may decide to study the chapters that give you the most difficulty early on in your test preparation. Each chapter in Sections 2 and 3 contains practice questions to drill you on the chapter’s main concepts. As you answer the hundreds of practice questions in this book, you will undoubtedly want to check your answers against the answer section at the end of each chapter. If, after answering all the questions in a section you feel you need more practice, reread the questions and try your hand at responding one more time. Repetition is often the key to success as studies show that most repetitive tasks become part of a person’s inventory of skills over time.

2

C H A P T E R

1

Civil Service Jobs

C

ivil service jobs range from clerical work to forestry, from social work to cartography, and from painting to nursing. The government workforce is diverse with career possibilities in a wide array of specialties and fields, including:

■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■

Accounting Administration Agriculture Air Traffic Control Biology Budgetary Work Cartography Chemistry Claims Work Clerical Work Conservation

■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■

Court Work Custodial Work Defense-related Work Drafting Educational Service Electrical Work Engineering Finance Firefighting Health Services Human Services 3

■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■

Information Technology Law Enforcement Legal Machinist Work Nursing Painting Postal Work Service Work Social Work Treasury Work Visa Examination

–CIVIL SER VICE JOBS–

may enter the government pay scale at different grades. For example, high school graduates may enter at GS2 (“GS” means “General Schedule”), whereas junior college graduates may enter at GS-4. Unlike jobs in the private sector, government job openings aren’t listed in the classified section of your city or local paper. But there are excellent, easily accessible sources of government job information. The Office of Personnel Management (OPM) updates a list of federal job vacancies daily. You can access this information 24 hours a day, 7 days a week by calling the OPM’s automated telephone system, Jobs by Phone, at 703–724–1850. Although this service offers around-the-clock convenience, beware: It may take more than one phone call to find exactly the information you need. The most user-friendly of the OPM resources, www.usajobs.opm.gov, allows you to search for jobs by region, state, zip code, country, and department. Use this website to print a copy of application forms and access information about pay scales. You can even create a resume online or electronically file your qualifications statement.

The government is the largest single employer in the United States. Government jobs are secure, have great holiday and vacation schedules, offer health insurance, and provide paid training for employees. Specific benefits include: ■ ■ ■ ■ ■ ■

■ ■ ■ ■

10 paid holidays a year 13 to 26 paid vacation days a year 13 sick days a year death and disability insurance group life insurance medical and dental benefits (including healthcare flexible spending accounts, HCFSAs) retirement benefits alternative work schedules government-paid training tuition reimbursement

Civilian government employees are grouped by the type of work they do. This is called the series. The level of their relative positions (based on difficulty) is called the grade. Each grade progresses upward through steps. The higher the step, the more money you will earn. Depending on your prior education, you

4

–CIVIL SER VICE JOBS –

FEDERAL PAY SCHEDULES, 2007 GRADE 1

2

ANNUAL RATES FOR STEPS (IN DOLLARS) 3 4 5 6 7 8

9

10

1

16,630

17,185

17,739

18,289

18,842

19,167

19,713

20,264

20,286

20,798

2

18,698

19,142

19,761

20,286

20,512

21,115

21,718

22,321

22,924

23,527

3

20,401

21,081

21,761

22,441

23,121

23,801

24,481

25,161

25,841

26,521

4

22,902

23,665

24,428

25,191

25,954

26,717

27,480

28,243

29,006

29,769

5

25,623

26,477

27,331

28,185

29,039

29,893

30,747

31,601

32,455

33,309

6

28,562

29,514

30,466

31,418

32,370

33,322

34,274

35,226

36,178

37,130

7

31,740

32,798

33,856

34,914

35,972

37,030

38,088

39,146

40,204

41,262

8

35,151

36,323

37,495

38,667

39,839

41,011

42,183

43,355

44,527

45,699

9

38,824

40,118

41,412

42,706

44,000

45,294

46,588

47,882

49,176

50,470

10

42,755

44,180

45,605

47,030

48,455

49,880

51,305

52,730

54,155

55,580

11

46,974

48,540

50,106

51,672

53,238

54,804

56,370

57,936

59,502

61,068

12

56,301

58,178

60,055

61,932

63,809

65,686

67,563

69,440

71,317

73,194

13

66,951

69,183

71,415

73,647

75,879

78,111

80,343

82,575

84,807

87,039

14

79,115

81,752

84,389

87,026

89,663

92,300

94,937

97,574

100,211 102,848

15

93,063

96,165

99,267

102,369 105,471 108,573 111,675 114,777 117,879 120,981

Please note that GS pay is adjusted according to your geographic location, so the majority of jobs pay more than the base salary listed in this table. The amount in the Base GS Pay Scale is multiplied by the percentage adjustment and the result is then added to the base pay. Also, certain hard-to-fill jobs, usually in the scientific, technical, and medical fields, may have higher starting salaries. Exact pay information can be found on position vacancy announcements. Source: U.S. Office of Personnel Management, January 2007.

5

C H A P T E R

2

The LearningExpress Test Preparation System

T

aking any test can be tough. But don’t let the written test scare you! If you prepare ahead of time, you can achieve a top score. The LearningExpress Test Preparation System, developed exclusively for LearningExpress by leading test experts, gives you the discipline and attitude you need to be a winner. Getting ready for any test takes work. If you plan to obtain an entry-level civil service position, you will have to score well on your civil service exam. This book focuses specifically on the math and vocabulary skills that you will be tested on—two areas that have proven difficult for many test takers. By honing in on these skills, you will take your first step toward achieving the career of your dreams. However, there are all sorts of pitfalls that can prevent you from doing your best on exams. Here are some obstacles that can stand in the way of your success.

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–THE LEARNINGEXPRESS TEST PREPARATION SYSTEM–

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Step 1. Get Information Step 2. Conquer Test Anxiety Step 3. Make a Plan Step 4. Learn to Manage Your Time Step 5. Learn to Use the Process of Elimination Step 6. Know When to Guess Step 7. Reach Your Peak Performance Zone Step 8. Get Your Act Together Step 9. Do It! Total

being unfamiliar with the format of the exam being paralyzed by test anxiety leaving your preparation to the last minute not preparing at all not knowing vital test-taking skills like: ■ how to pace yourself through the exam ■ how to use the process of elimination ■ when to guess not being in tip-top mental and physical shape forgetting to eat breakfast and having to take the exam on an empty stomach forgetting a sweater or jacket and shivering through the exam

30 20 50 10

minutes minutes minutes minutes

20 minutes 20 minutes 10 10 10 3

minutes minutes minutes hours

We estimate that working through the entire system will take you approximately three hours, though it’s perfectly OK if you work faster or slower than the time estimates say. If you can take a whole afternoon or evening, you can work through the entire LearningExpress Test Preparation System in one sitting. Otherwise, you can break it up, and do just one or two steps a day for the next several days. It’s up to you— remember, you’re in control.

What’s the common denominator in all these test-taking pitfalls? One word: control. Who’s in control, you or the exam? Now the good news: The LearningExpress Test Preparation System puts you in control. In just nine easy-to-follow steps, you will learn everything you need to know to make sure you are in charge of your preparation and performance on the exam. Other test takers may let the test get the better of them; other test takers may be unprepared or out of shape, but not you. You will have taken all the steps you need to take for a passing score. Here’s how the LearningExpress Test Preparation System works: Nine easy steps lead you through everything you need to know and do to get ready to master your exam. Each of the steps gives you tips and activities to help you prepare for any exam. It’s important that you follow the advice and do the activities, or you won’t be getting the full benefit of the system. Each step gives you an approximate time estimate.



Step 1: Get Information

Time to complete: 30 minutes Activities: Read Section 1, “Preparing for Your Civil Service Exam” and Chapter 1, “Civil Service Jobs.” If you haven’t already done so, stop here and read Section 1 and Chapter 1 of this book. Here, you’ll learn how to use this book, see an overview of the range of civil service jobs, and be presented with a discussion regarding earnings and job searches. Knowledge is power. The first step in the LearningExpress Test Preparation System is finding out everything you can about the types of questions that will be asked on any math and vocabulary section of the civil service exam. Practicing and studying the

8

–THE LEARNINGEXPRESS TEST PREPARATION SYSTEM–

formance on the exam itself, but it can even keep you from preparing! In Step 2, you’ll learn stress management techniques that will help you succeed on your exam. Learn these strategies now, and practice them as you work through the practice tests in this book, so they’ll be second nature to you by exam day.

exercises in this book will help prepare you for those tests. Math topics that are tested include: ■ ■ ■ ■ ■ ■ ■ ■ ■

arithmetic, powers, and roots fractions decimals percents number series word problems charts, tables, and graphs algebra geometry and measurement

Combating Test Anxiety

The first thing you need to know is that a little test anxiety is a good thing. Everyone gets nervous before a big exam—and if that nervousness motivates you to prepare thoroughly, so much the better. It’s said that Sir Laurence Olivier, one of the foremost British actors of last century, was ill before every performance. His stage fright didn’t impair his performance; in fact, it probably gave him a little extra edge—just the kind of edge you need to do well, whether on a stage or in an exam room. On page 11 is the Test Stress Test. Stop here and answer the questions on that page to find out whether your level of test anxiety is something you should worry about.

Vocabulary topics that are tested include: ■ ■ ■ ■ ■ ■

vocabulary in context reading comprehension synonyms antonyms grammar spelling

After completing the LearningExpress Test Preparation System, you will then begin to apply the test-taking strategies you learn as you work through practice questions in these topic areas (Chapters 3 through 14). You can see how well your training paid off in Chapters 15 and 16, where you will take two practice civil service tests.



Stress Management before the Test

If you feel your level of anxiety getting the best of you in the weeks before the test, here is what you need to do to bring the level down again: ■

Step 2: Conquer Test Anxiety

Time to complete: 20 minutes Activity: Take the Test Stress Test Having complete information about the exam is the first step in getting control of the exam. Next, you have to overcome one of the biggest obstacles to test success: test anxiety. Test anxiety not only impairs your per-

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9

Get prepared. There’s nothing like knowing what to expect. Being prepared will put you in control of test anxiety. That’s why you’re reading this book. Use it faithfully, and remind yourself that you’re better prepared than most of the people taking the test. Practice self-confidence. A positive attitude is a great way to combat test anxiety. This is no time to be humble or shy. Stand in front of the mirror and say to your reflection, “I’m prepared. I’m full of self-confidence. I’m going to ace this test. I

–THE LEARNINGEXPRESS TEST PREPARATION SYSTEM–

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Now close your eyes and imagine you’re actually there. If you practice in advance, you’ll find that you need only a few seconds of this exercise to experience a significant increase in your sense of well-being.

know I can do it.” Say it into a recorder and play it back once a day. If you hear it often enough, you’ll believe it. Fight negative messages. Every time someone starts telling you how hard the exam is or how it’s almost impossible to get a high score, start telling them your self-confidence messages. If the someone with the negative messages is you, telling yourself you don’t do well on exams and you just can’t do this, don’t listen. Listen to your self-confidence messages instead. Visualize. Imagine yourself reporting for your first day on the job. Visualizing success can help make it happen—and it reminds you why you’re preparing for the exam so diligently. Exercise. Physical activity helps calm down your body and focus your mind. Besides, being in good physical shape can actually help you do well on the exam. Go for a run, lift weights, go swimming—and do it regularly.

When anxiety threatens to overwhelm you right there during the exam, there are still things you can do to manage your stress level: ■

■

■

Stress Management on Test Day

There are several ways you can bring down your level of test anxiety on test day. To find a comfort level, experiment with the following exercises in the weeks before the test, and use the ones that work best for you. ■

■

■

■

Deep breathing. Take a deep breath while you count to five. Hold it for a count of one, then let it out on a count of five. Repeat several times. Move your body. Try rolling your head in a circle. Rotate your shoulders. Shake your hands from the wrist. Many people find these movements very relaxing. Visualize again. Think of the place where you are most relaxed: lying on the beach in the sun, walking through the park, or sipping a cup of hot tea.

Repeat your self-confidence messages. You should have them memorized by now. Say them silently to yourself, and believe them! Visualize one more time. This time, visualize yourself moving smoothly and quickly through the test answering every question right and finishing just before time is up. Like most visualization techniques, this one works best if you’ve practiced it ahead of time. Find an easy question. Skim over the test until you find an easy question, and then answer it. Filling in even one circle gets you into the testtaking groove. Take a mental break. Everyone loses concentration once in a while during a long test. It’s normal, so you shouldn’t worry about it. Instead, accept what has happened. Say to yourself, “Hey, I lost it there for a minute. My brain is taking a break.” Put down your pencil, close your eyes, and do some deep breathing for a few seconds. Then you’re ready to go back to work.

Try these techniques ahead of time, and see if they work for you!

10

Test Stress Test You only need to worry about test anxiety if it is extreme enough to impair your performance. The following questionnaire will provide a diagnosis of your level of test anxiety. In the blank before each statement, write the number that most accurately describes your experience. 0 = never 1 = once or twice 2 = sometimes 3 = often I have gotten so nervous before an exam that I simply put down the books and didn’t study for it. I have experienced disabling physical symptoms such as vomiting and severe headaches because I was nervous about an exam. I have simply not showed up for an exam because I was scared to take it. I have experienced dizziness and disorientation while taking an exam. I have had trouble filling in the little circles because my hands were shaking too hard. I have failed an exam because I was too nervous to complete it. Total: Add up the numbers in the blanks. Your Test Stress Score Here are the steps you should take, depending on your score. If you scored: ■

Below 3, your level of test anxiety is nothing to worry about; it’s probably just enough to give you the motivation to excel.

■

Between 3 and 6, your test anxiety may be enough to impair your performance, and you should practice the stress management techniques listed in this chapter to try to bring your test anxiety down to manageable levels.

■

Above 6, your level of test anxiety is a serious concern. In addition to practicing the stress management techniques listed in this chapter, you may want to seek additional, personal help. Call your local high school or community college and ask for the academic counselor. Tell the counselor that you have a level of test anxiety that sometimes keeps you from being able to take an exam. The counselor may be willing to help you or may suggest someone else you should talk to.

11

–THE LEARNINGEXPRESS TEST PREPARATION SYSTEM–



Step 3: Make a Plan

Even more important than making a plan is making a commitment. You can’t review everything you need to know for a civil service exam in one night. You have to set aside some time every day for study and practice. Try for at least 20 minutes a day. Twenty minutes daily will do you much more good than two hours on Saturday. Don’t put off your study until the day before the exam. Start now. A few minutes a day, with half an hour or more on weekends can make a big difference in your score. If you have months before the exam, you’re lucky. Don’t put off your studying until the week before the exam! Start now. Even ten minutes a day, with half an hour or more on weekends, can make a big difference in your score—and in your chances of making the grade you want!

Time to complete: 50 minutes Activity: Construct a study plan Maybe the most important thing you can do to get control of yourself and your exam is to make a study plan. Too many people fail to prepare simply because they fail to plan. Spending hours on the day before the exam poring over sample test questions not only raises your level of test anxiety, it is also no substitute for careful preparation and practice. Don’t fall into the cram trap. Take control of your preparation time by mapping out a study schedule. If you’re the kind of person who needs deadlines and assignments to motivate you for a project, here they are. If you’re the kind of person who doesn’t like to follow other people’s plans, you can use the suggested schedules here to construct your own.

Schedule A: The 30-Day Plan

If you have at least one month before you take your test, you have plenty of time to prepare—as long as you don’t procrastinate! If you have less than a month, turn to Schedule B. TIME

Day 1

PREPARATION

Read Section 1 of this book. Also, skim over any written materials you may have about the civil service exam.

Day 2

Read Chapter 3, “Arithmetic, Powers, and Roots.” Work through practice questions 1–50. Score yourself.

Day 3

Review any Chapter 3 concepts you feel are necessary for you to brush up on.

Day 4

Read Chapter 4, “Fractions and Decimals.” Work through practice questions 1–50. Score yourself.

Day 5

Read Chapter 5, “Percents.” Work through practice questions 1–49. Score yourself.

Day 6

Review any Chapter 4 or Chapter 5 concepts you feel are necessary for you to brush up on.

Day 7

Read Chapter 6, “Number Series and Analogies.” Work through practice questions 1–50. Score yourself.

Day 8

Review any Chapter 6 concepts you feel are necessary for you to brush up on.

Day 9

Read Chapter 7, “Word Problems.” Work through practice questions 1–50. Score yourself. 12

–THE LEARNINGEXPRESS TEST PREPARATION SYSTEM–

TIME

PREPARATION

Day 10

Review any Chapter 7 concepts you feel are necessary for you to brush up on.

Day 11

Read Chapter 8, “Charts, Tables, and Graphs.” Work through practice questions 1–50. Score yourself.

Day 12

Review any Chapter 8 concepts you feel are necessary for you to brush up on.

Day 13

Read Chapter 9, “Measurement and Geometry.” Work through practice questions 1–50. Score yourself.

Day 14

Review any Chapter 9 concepts you feel are necessary for you to brush up on. Turn to “Section 5: Helpful Resources” and read through the Glossary of Math Terms and the Math Formula Sheet. If you choose, make index cards for unfamiliar items.

Day 15

Read Chapter 10, “Vocabulary in Context.” Work through the practice exercises and questions. Score yourself.

Day 16

Review any Chapter 10 concepts you feel are necessary for you to brush up on.

Day 17

Read Chapter 11, “Synonyms and Antonyms.” Work through practice questions 1–50. Score yourself.

Day 18

Review any Chapter 11 concepts you feel are necessary for you to brush up on.

Day 19

Read Chapter 12, “Reading Comprehension.” Work through practice questions 1–50. Score yourself.

Day 20

Review any Chapter 12 concepts you feel are necessary for you to brush up on.

Day 21

Read Chapter 13, “Grammar.” Work through practice questions 1–50. Score yourself.

Day 22

Review any Chapter 13 concepts you feel are necessary for you to brush up on.

Day 23

Read Chapter 14, “Spelling.” Work through practice questions 1–50. Score yourself.

Day 24

Review any Chapter 14 concepts you feel are necessary for you to brush up on. Turn to “Section 5: Helpful Resources” and read through the Commonly Tested Vocabulary Words and Prefixes, Suffixes, and Word Roots appendices. If you choose, make index cards for unfamiliar terms or concepts.

Day 25

In Chapter 15, take Practice Test 1. Score yourself and review any incorrect questions.

Day 26

Review any concepts you feel are necessary for you to brush up on. Work through similar questions in the appropriate chapters.

Day 27

In Chapter 16, take Practice Test 2. Score yourself and review any incorrect questions.

Day 28

Review any concepts you feel are necessary for you to brush up on. Work through similar questions in the appropriate chapters.

Day 29

Review the chapters that contain the topics you were weak on during the Practice Exams.

Day before the exam Relax. Do something unrelated to the exam and go to bed at a reasonable hour.

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–THE LEARNINGEXPRESS TEST PREPARATION SYSTEM–

Schedule B: The 14-Day Plan

If you have two weeks or less before the exam, you may have your work cut out for you. Use this 14-day schedule to help you make the most of your time. TIME

PREPARATION

Day 1

Read Chapters 1 and 2.

Day 2

Complete Chapters 3, 4, and 5, including the practice questions.

Day 3

Complete Chapters 6 and 7, including the practice questions.

Day 4

Complete Chapters 8 and 9, including the practice questions.

Day 5

Review the math chapters that contained the topics in which you were weak, in addition to the helpful resources geared for math review.

Day 6

Complete Chapter 10, including the practice questions.

Day 7

Complete Chapters 11 and 12, including the practice questions.

Day 8

Complete Chapters 13 and 14, including the practice questions.

Day 9

Review the vocabulary chapters that contained the topics in which you were weak, in addition to the helpful resources geared for vocabulary review.

Day 10 Day 11

Complete Practice Test 1 (Chapter 15) and score yourself. Review all of the questions that you missed. Review any concepts you feel are necessary for you to brush up on. Work through similar questions in the appropriate chapters.

Day 12

Complete Practice Test 2 (Chapter 16) and score yourself. Review all of the questions that you missed.

Day 13

Review any topics as indicated by the questions you missed on the practice tests. Then, look at the questions you missed again and make sure you understand them.

Day before Relax. Do something unrelated to the exam and go to bed at a reasonable hour. the exam



Step 4: Learn to Manage Your Time

strategies as you take the sample tests in this book, and then you’ll be ready to use them on test day. First, take control of your time on the exam. Civil service exams have a time limit, which may give you more than enough time to complete all the questions—or not enough time. It’s a terrible feeling to hear the examiner say,“Five minutes left,“ when you’re only three-quarters of the way through the test. Here are some tips to keep that from happening to you.

Time to complete: 10 minutes to read, many hours of practice! Activities: Use these strategies as you take the practice tests in this book Steps 4, 5, and 6 of the LearningExpress Test Preparation System put you in charge of your exam by showing you test-taking strategies that work. Practice these 14

–THE LEARNINGEXPRESS TEST PREPARATION SYSTEM–

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Follow directions. If the directions are given orally, listen closely. If they’re written on the exam booklet, read them carefully. Ask questions before the exam begins if there is anything you don’t understand. If you’re allowed to write in your exam booklet, write down the beginning time and ending time of the exam. Pace yourself. Glance at your watch every few minutes, and compare the time to how far you’ve gotten in the test. When one-quarter of the time has elapsed, you should be a quarter of the way through the section, and so on. If you’re falling behind, pick up the pace a bit. Keep moving. Don’t waste time on one question.If you don’t know the answer,skip the question and move on.Circle the number of the question in your test booklet in case you have time to come back to it later. Keep track of your place on the answer sheet. If you skip a question, make sure you skip on the answer sheet too. Check yourself every 5–10 questions to make sure the question number and the answer sheet number are still the same. Don’t rush. Although you should keep moving, rushing won’t help. Try to keep calm and work methodically and quickly.

Choosing the Right Answer by

Step 5: Learn to Use the Process of Elimination

Whatever you do, don’t waste time with any one answer choice. If you can’t figure out what an answer choice means, don’t worry about it. If it’s the right answer, you’ll probably be able to eliminate all the others, and, if it’s the wrong answer, another answer will probably strike you more obviously as the right answer.

Process of Elimination

As you read a question,you may find it helpful to underline important information or make some notes about what you’re reading. When you get to the heart of the question, circle it and make sure you understand what it is asking. If you’re not sure of what’s being asked, you’ll never know whether you’ve chosen the right answer.What you do next depends on the type of question you’re answering. ■

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Time to complete: 20 minutes Activity: Complete worksheet on Using the Process of Elimination After time management, your most important tool for taking control of your exam is using the process of elimination wisely. It’s standard test-taking wisdom that you should always read all the answer choices before choosing your answer. This helps you find the right answer by eliminating wrong answer choices. And, sure enough, that standard wisdom applies to your exam, too.

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15

If it’s math, take a quick look at the answer choices for some clues. Sometimes this helps to put the question in a new perspective and makes it easier to answer. Then make a plan of attack to solve the problem. Otherwise, follow this simple process-of-elimination plan to manage your testing time as efficiently as possible: Read each answer choice and make a quick decision about what to do with it, marking your test book accordingly: ■ The answer seems reasonable; keep it. Put a ✔ next to the answer. ■ The answer is awful. Get rid of it. Put an X next to the answer. ■ You can’t make up your mind about the answer, or you don’t understand it. Keep it for now. Put a ? next to it.

If you haven’t eliminated any answers at all, skip the question temporarily, but don’t forget to mark the question so you can come back to it later if you have time. If the test has no penalty for wrong answers, and you’re certain you could

–THE LEARNINGEXPRESS TEST PREPARATION SYSTEM–

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fourth of a point for each wrong answer. If you cannot eliminate any of the answer choices, you’re better off leaving the answer blank because the odds of guessing correctly are one in five. However, if you can eliminate two of the choices as definitely wrong, the odds are now in your favor. You have a one in three chance of answering the question correctly. Fortunately, few tests are scored using such elaborate means, but if your test is one of them, know the penalties and calculate your odds before you take a guess on a question.

never answer this question in a million years, pick an answer and move on! If you’ve eliminated all but one answer, just reread the circled part of the question to make sure you’re answering exactly what’s asked. Mark your answer sheet and move on to the next question. Here’s what to do when you’ve eliminated some, but not all of the answer choices. Compare the remaining answers looking for similarities and differences, reasoning your way through these choices. Try to eliminate those choices that don’t seem as strong to you. But don’t eliminate an answer just because you don’t understand it. You may even be able to use relevant information from other parts of the test. If you’ve narrowed it down to a single answer, check it against the circled question to be sure you’ve answered it. Then mark your answer sheet and move on. If you’re down to only two or three answer choices, you’ve improved your odds of getting the question right. Make an educated guess and move on. However, if you think you can do better with more time, mark the question as one to return to later.

If You Finish Early

Use any time you have left to do the following: ■

■

■

If You’re Penalized for Wrong

■

Answers

You must know whether you’ll be penalized for wrong answers before you begin the civil service exam. If you don’t, ask the proctor before the test begins. Whether you make a guess or not depends upon the penalty. Some standardized tests are scored in such a way that every wrong answer reduces your score by a fraction of a point, and these can really add up against you! Whatever the penalty, if you can eliminate enough choices to make the odds of answering the question better than the penalty for getting it wrong, make a guess. This is called educated guessing. Let’s imagine you are taking a test in which each answer has five choices and you are penalized one-

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Go back to questions you marked to return to later and try them again. Check your work on all the other questions. If you have a good reason for thinking a response is wrong, change it. Review your answer sheet. Make sure you’ve put the answers in the right places and you’ve marked only one answer for each question. (Most tests are scored in such a way that questions with more than one answer are marked wrong.) If you’ve erased an answer, make sure you’ve done a good job of it. Check for stray marks on your answer sheet that could distort your score.

Whatever you do,don’t waste time when you’ve finished a test section.Make every second count by checking your work over and over again until time is called. Try using your powers of elimination on the questions in the worksheet on page 17 called “Using the Process of Elimination.” The answer explanations that follow show one possible way you might use the process to arrive at the right answer. The process of elimination is your tool for the next step, which is knowing when to guess.

16

Using the Process of Elimination Use the process of elimination to answer the following questions.

1. Ilsa is as old as Meghan will be in five years.

3. Smoking tobacco has been linked to

The difference between Ed’s age and Meghan’s

a. an increased risk of stroke and heart attack.

age is twice the difference between Ilsa’s age

b. all forms of respiratory disease.

and Meghan’s age. Ed is 29. How old is Ilsa?

c. increasing mortality rates over the past ten

a. 4

years.

b. 10

d. juvenile delinquency.

c. 19

4. Which of the following words is spelled

d. 24

correctly?

2. “All drivers of commercial vehicles must carry a

a. incorrigible

valid commercial driver’s license whenever

b. outragous

operating a commercial vehicle.” According to

c. domestickated

this sentence, which of the following people

d. understandible

need NOT carry a commercial driver’s license? a. a truck driver idling his engine while waiting to be directed to a loading dock b. a bus operator backing her bus out of the way of another bus in the bus lot c. a taxi driver driving his personal car to the grocery store d. a limousine driver taking the limousine to her home after dropping off her last passenger of the evening

17

Using the Process of Elimination (continued) Answers Here are the answers, as well as some suggestions as to how you might have used the process of elimination to find them.

1. d. You should have eliminated choice a immedi-

3. a. You could eliminate choice b simply because

ately. Ilsa can’t be four years old if Meghan is

of the presence of the word all. Such

going to be Ilsa’s age in five years. The best

absolutes hardly ever appear in correct

way to eliminate other answer choices is to

answer choices. Choice c looks attractive

try plugging them in to the information given

until you think a little about what you know—

in the problem. For instance, for choice b, if

aren’t fewer people smoking these days,

Ilsa is 10, then Meghan must be 5. The differ-

rather than more? So how could smoking be

ence in their ages is 5. The difference

responsible for a higher mortality rate? (If you

between Ed’s age, 29, and Meghan’s age, 5,

didn’t know that mortality rate means the rate

is 24. Is 24 two times 5? No. Then choice b is

at which people die, you might keep this

wrong. You could have eliminated choice c in

choice as a possibility, but you’d still be able

the same way and be left with choice d.

to eliminate two answers and have only two

2. c. Note the word not in the question, and go

to choose from.) Choice d can’t be proven,

through the answers one by one. Is the truck

so you could eliminate that one, too. Now

driver in choice a “operating a commercial

you’re left with the correct choice, a.

vehicle”? Yes, idling counts as “operating,”

4. a. How you used the process of elimination

so he needs to have a commercial driver’s

here depends on which words you recog-

license. Likewise, the bus operator in choice

nized as being spelled incorrectly. If you

b is operating a commercial vehicle; the

knew that the correct spellings were outra-

question doesn’t say the operator has to be

geous, domesticated, and understandable,

on the street. The limo driver in choice d is

then you were home free. Surely you knew

operating a commercial vehicle, even if it

that at least one of those words was wrong.

doesn’t have a passenger in it. However, the taxi driver in choice c is not operating a commercial vehicle, but his own private car.

18

–THE LEARNINGEXPRESS TEST PREPARATION SYSTEM–



Step 6: Know When to Guess

and your “guessing intutition.” There are two things you need to know about yourself before you go into the exam:

Time to complete: 20 minutes Activity: Complete worksheet on Your Guessing Ability Armed with the process of elimination, you’re ready to take control of one of the big questions in test-taking: Should I guess? The first and main answer is, it depends on the scoring rules of the test and if you’re able to eliminate any answers. Some exams have what’s called a “guessing penalty,” in which a fraction of your wrong answers is subtracted from your right answers. Check with the administrators of your particular exam to see if this is the case. In many instances, the number of questions you answer correctly yields your raw score. So you have nothing to lose and everything to gain by guessing. The more complicated answer to the question, “Should I guess?” depends on you, your personality,

1. Are you a risk-taker? 2. Are you a good guesser? You’ll have to decide about your risk-taking quotient on your own. To find out if you’re a good guesser, complete the worksheet called “Your Guessing Ability” that begins on page 20. Frankly, even if you’re a play-it-safe person with terrible intuition, you’re still safe in guessing every time, as long as your exam has no guessing penalty. The best thing would be if you could overcome your anxieties and go ahead and mark an answer. But you may want to have a sense of how good your intuition is before you go into the exam.

19

Your Guessing Ability The following are ten really hard questions. You’re not supposed to know the answers. Rather, this is an assessment of your ability to guess when you don’t have a clue. Read each question carefully, just as if you did expect to answer it. If you have any knowledge at all of the subject of the question, use that knowledge to help you eliminate wrong answer choices. Use this answer grid to fill in your answers to the questions.

[Insert 1-10, a-d Answer Grid] 1. September 7 is Independence Day in

5. Which of the following is NOT one of the Five

a. India.

Classics attributed to Confucius?

b. Costa Rica.

a. the I Ching

c. Brazil.

b. the Book of Holiness

d. Australia.

c. the Spring and Autumn Annals d. the Book of History

2. Which of the following is the formula for deter6. The religious and philosophical doctrine that

mining the momentum of an object? a. p = mv

holds that the universe is constantly in a strug-

b. F = ma

gle between good and evil is known as

c. P = IV

a. pelagianism.

d. E =

mc2

b. manichaeanism. c. neo-Hegelianism.

3. Because of the expansion of the universe, the

d. epicureanism.

stars and other celestial bodies are all moving

7. The third chief justice of the U.S. Supreme

away from each other. This phenomenon is known as

Court was

a. Newton’s first law.

a. John Blair.

b. the big bang.

b. William Cushing.

c. gravitational collapse.

c. James Wilson.

d. Hubble flow.

d. John Jay.

4. American author Gertrude Stein was born in

8. Which of the following is the poisonous portion

a. 1713.

of a daffodil?

b. 1830.

a. the bulb

c. 1874.

b. the leaves

d. 1901.

c. the stem d. the flowers

20

Your Guessing Ability (continued) 9. The winner of the Masters golf tournament in

Answers

1953 was

Check your answers against the correct answers.

a. Sam Snead.

1. c. 2. a. 3. d. 4. c. 5. b. 6. b. 7. b. 8. a. 9. d. 10. a.

b. Cary Middlecoff. c. Arnold Palmer. d. Ben Hogan.

10. The state with the highest per capita personal income in 1980 was a. Alaska. b. Connecticut. c. New York. d. Texas.

How Did You Do? You may have simply gotten lucky and actually known the answer to one or two questions. In addition, your guessing was more successful if you were able to use the process of elimination on any of the questions. Maybe you didn’t know who the third chief justice was (question 7), but you knew that John Jay was the first. In that case, you would have eliminated choice d and therefore improved your odds of guessing right from one in four to one in three. According to probability, you should get two and a half answers correct, so getting either two or three right would be average. If you got four or more right, you may be a really terrific guesser. If you got one or none right, you may decide not to guess. Keep in mind, though, that this is only a small sample. You should continue to keep track of your guessing ability as you work through the sample questions in this book. Circle the numbers of questions you guess; or, if you don’t have time during the practice tests, go back afterward and try to remember which questions you guessed. Remember, on a test with four answer choices, your chances of getting a right answer is one in four. So keep a separate “guessing” score for each exam. How many questions did you guess? How many did you get right? If the number you got right is at least one-fourth of the number of questions you guessed, you are at least an average guesser, maybe better—and you should always go ahead and guess on the real exam. If the number you got right is significantly lower than one-fourth of the number you guessed on, you should not guess on exams where there is a guessing penalty unless you can eliminate a wrong answer. If there’s no guessing penalty, you would be safe in guessing anyway, but maybe you’d feel more comfortable if you guessed only selectively, when you can eliminate a wrong answer or at least have a good feeling about one of the answer choices.

21

–THE LEARNINGEXPRESS TEST PREPARATION SYSTEM–



Step 7: Reach Your Peak Performance Zone

What your body needs for peak performance is simply a balanced diet. Eat plenty of fruits and vegetables, along with protein and complex carbohydrates. Foods that are high in lecithin (an amino acid), such as fish and beans, are especially good “brain foods.”

Time to complete: 10 minutes to read; weeks to complete! Activity: Complete the Physical Preparation Checklist To get ready for a challenge like a big exam, you have to take control of your physical, as well as your mental state. Exercise, proper diet, and rest will ensure that your body works with, rather than against, your mind on test day, as well as during your preparation.

Rest

You probably know how much sleep you need every night to be at your best, even if you don’t always get it. Make sure you do get that much sleep, though, for at least a week before the exam. Moderation is important here, too. Extra sleep will just make you groggy. If you’re not a morning person and your exam will be given in the morning, you should reset your internal clock so that your body doesn’t think you’re taking an exam at 3 A.M. You have to start this process well before the exam. The way it works is to get up half an hour earlier each morning, and then go to bed half an hour earlier that night. Don’t try it the other way around; you’ll just toss and turn if you go to bed early without getting up early. The next morning, get up another half an hour earlier, and so on. How long you will have to do this depends on how late you’re used to getting up. Use the “Physical Preparation Checklist” on pages 23–24 to make sure you’re in tip-top form.

Exercise

If you don’t already have a regular exercise program going, the time during which you’re preparing for an exam is actually an excellent time to start one. If you’re already keeping fit—or trying to get that way—don’t let the pressure of preparing for an exam fool you into quitting now. Exercise helps reduce stress by pumping wonderful good-feeling hormones called endorphins into your system. It also increases the oxygen supply throughout your body and your brain, so you’ll be at peak performance on test day. A half hour of vigorous activity—enough to break a sweat—every day should be your aim. If you’re really pressed for time, every other day is OK. Choose an activity you like and get out there and do it. Jogging with a friend always makes the time go faster as does listening to music. But don’t overdo it. You don’t want to exhaust yourself. Moderation is the key.



Step 8: Get Your Act Together

Time to complete: 10 minutes to read; time to complete will vary Activity: Complete Final Preparations worksheet Once you feel in control of your mind and body, you’re in charge of test anxiety, test preparation, and test-taking strategies. Now it’s time to make charts and gather the materials you need to take to the exam.

Diet

First of all, cut out the junk. Go easy on caffeine and nicotine, and eliminate alcohol and any other drugs from your system at least two weeks before the exam. Promise yourself a special treat the night after the exam, if need be.

22

Physical Preparation Checklist For the week before the test, write down what physical exercise you engaged in and for how long and what you ate for each meal. Remember, you’re trying for at least half an hour of exercise every other day (preferably every day) and a balanced diet that’s light on junk food. Exam minus 7 days Exercise:

for

minutes

for

minutes

for

minutes

Breakfast: Lunch: Dinner: Snacks: Exam minus 6 days Exercise: Breakfast: Lunch: Dinner: Snacks: Exam minus 5 days Exercise: Breakfast: Lunch: Dinner: Snacks:

Gather Your Materials

Don’t Skip Breakfast

The night before the exam, lay out the clothes you will wear and the materials you have to bring with you to the exam. Plan on dressing in layers because you won’t have any control over the temperature of the exam room. Have a sweater or jacket you can take off if it’s warm. Use the checklist on the worksheet entitled “Final Preparations” on page 25 to help you pull together what you’ll need.

Even if you don’t usually eat breakfast, do so on exam morning. A cup of coffee doesn’t count. Don’t eat doughnuts or other sweet foods, either. A sugar high will leave you with a sugar low in the middle of the exam. A mix of protein and carbohydrates is best: Cereal with milk or eggs with toast will do your body a world of good.

23

Physical Preparation Checklist Exam minus 4 days Exercise:

for

minutes

for

minutes

for

minutes

for

minutes

Breakfast: Lunch: Dinner: Snacks: Exam minus 3 days Exercise: Breakfast: Lunch: Dinner: Snacks: Exam minus 2 days Exercise: Breakfast: Lunch: Dinner: Snacks: Exam minus 1 day Exercise: Breakfast: Lunch: Dinner: Snacks:



Step 9: Do It!

what to bring with you. In other words, you’re better prepared than most of the other people taking the test with you. You’re psyched! Just one more thing. When you’re done with the exam, you will have earned a reward. Plan a night out. Call your friends and plan a party, or have a nice dinner for two—whatever your heart desires. Give yourself something to look forward to.

Time to complete: 10 minutes, plus test-taking time Activity: Ace Your Test! Fast-forward to exam day. You’re ready. You made a study plan and followed through. You practiced your test-taking strategies while working through this book. You’re in control of your physical, mental, and emotional state. You know when and where to show up and

24

Final Preparations Getting to the Exam Site Location of exam: Date of exam: Time of exam: Do I know how to get to the exam site? Yes

No

If no, make a trial run. Time it will take to get to the exam site: Things to lay out the night before Clothes I will wear Sweater/jacket Watch Photo ID Admission card 4 no. 2 pencils

exam day. You’re ready to succeed. So do it. Go in there and ace the civil service exam! And, then, look forward to your new career.

And then do it. Go into the exam, full of confidence, armed with test-taking strategies you’ve practiced until they’re second nature. You’re in control of yourself, your environment, and your performance on

25

S E C T I O N

2

Math Prep for Civil Service Exams

N

ot all civil service exams test your math knowledge, but many do. The math portion of the civil service exam covers subjects you probably studied in grade school and high school. Knowledge of basic arithmetic, as well as the complex reasoning necessary for algebra, are important qualifications for almost any profession. You have to be able to add up dollar figures, evaluate budgets, compute percentages, and perform similar math tasks in many civil service positions. Many jobs require someone able to understand and interpret data presented in the form of tables and graphs. So even if your exam doesn’t include math, you’ll probably need to review the material in this section to be successful on the job. Before you begin working your way through Section 2, take a look at the following math strategies. These suggestions are tried and true, and will help you as you maneuver through this book. You may use one or all of them. Or, you may decide to pick and choose the combination that works best for you.

27

–MATH PREP FOR CIVIL SER VICE EXAMS–

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It’s best not to work in your head! Use your test book or scratch paper to take notes, draw pictures, and calculate. Although you might think that you can solve math questions more quickly in your head, that’s a good way to make mistakes. Instead, write out each step. Before you begin to make your calculations, read a math question in chunks rather than straight through from beginning to end. As you read each chunk, stop to think about what it means. Then make notes or draw a picture to represent that chunk. When you get to the actual question, circle it. This will keep you more focused as you solve the problem. Glance at the answer choices for clues. If they’re fractions, you should do your work in fractions; if they’re decimals, you should work in decimals, and so on. Make a plan of attack to help you solve the problem.

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28

When you get your answer, reread the circled question to make sure you’ve answered it. This helps avoid the careless mistake of answering the wrong question. Check your work after you get an answer. Test takers get a false sense of security when they get an answer that matches one of the multiplechoice answers. It could be right, but you should always check your work. Remember to: ■ Ask yourself if your answer is reasonable, if it makes sense. ■ Plug your answer back into the problem to make sure the problem holds together. ■ Do the question a second time, but use a different method. ■ Approximate when appropriate. For example: $5.98 + $8.97 is a little less than $15 (Add $6 + $9). 0.9876 × 5.0342 is close to 5 (Multiply 1 × 5). Skip hard questions and come back to them later. Mark them in your test book so you can find them quickly.

C H A P T E R

3

Arithmetic, Powers, and Roots

Y

ou may have forgotten what the term arithmetic encompasses, but you most likely use it every day. Arithmetic consists of the following four familiar operations:

■ ■ ■ ■

addition subtraction multiplication division

When solving arithmetic problems, it’s helpful to keep in mind the following definitions regarding the operations:

29

–ARITHMETIC, POWERS, AND ROOTS–

■ ■ ■ ■

A sum is obtained by adding. A difference is obtained by subtracting. A product is obtained by multiplying. A quotient is obtained by dividing.

Basic arithmetic problems require you to add, subtract, multiply, or divide. You may be asked to find the sum, difference, product, or quotient. More advanced arithmetic questions deal with combined operations. This simply means that two or more of the basic operations are combined into an equation or expression. For example, a question that has you find the product of two sums would be considered a combined operations question. When dealing with basic arithmetic and combined operations, it is helpful to understand three basic number laws: the commutative law, the associative law, and the distributive law. Sometimes these three laws are referred to as properties (such as the commutative property). ■

■

■

The commutative law applies to addition and multiplication and can be represented as a + b = b + a or a × b = b × a. For example, 2 + 3 = 3 + 2 and 4 × 2 = 2 × 4 exhibit the commutative law. The associative law applies to grouping of addition or multiplication equations and expressions. It can be represented as a + (b + c) = (a + b) + c or a × (b × c) = (a × b) × c. For example, 10 + (12 + 14) = (10 + 12) + 14. The distributive law applies to multiplication over addition and can be represented as a(b + c) = ab + ac. For example, 3(5 + 7) = 3 × 5 + 3 × 7.

It is also especially important to understand the order of operations. When dealing with a combination of operations, you must perform the operations in a particular order. An easy way to remember the order of operations is to use the mnemonic PEMDAS, where each letter stands for an operation: ■ ■ ■ ■



Parentheses: Always calculate the values inside the parentheses first. Exponents: Exponents (or powers) are calculated second. Multiplication/Division: Third, multiply or divide in order from left to right. Addition/Subtraction: Last, add or subtract in order from left to right.

Powers

When you raise a number (the base) to an exponent, this is sometimes called raising the number to a power. Basepower or Baseexponent If the terms have different bases, you cannot combine them. When you have the same base, it is easy to combine the exponents according to the following rules:

30

–ARITHMETIC, POWERS, AND ROOTS–

■ ■ ■ ■

When multiplying like bases, such as ax × ay, simply add the exponents: ax × ay = ax + y When dividing, such as ax ÷ ay, simply subtract the exponents: ax ÷ ay = ax – y When raising a power to a power, such as (ax)y, simply multiply the exponents: (ax)y = axy If one of the bases doesn’t have an exponent written, that means its exponent is 1: a = a1

Note that if more than one base is included in the parentheses, you must raise all of the bases to the power outside the parentheses, so (axby)z = axzbyz. (abx)y equals aybxy because a is equal to a1. Two common powers have special names. When raising a number to the second power, it is called squaring the number. When raising a number to the third power, it is called cubing the number. Let’s take a look at (62)5. Remember, when raising a power to a power, you can just multiply the exponents. Here you should multiply 2 × 5, so (62)5 = 62 × 5 = 610. You can check your work by writing out the solution: (62)5 = (6 × 6)5 = (6 × 6)(6 × 6)(6 × 6)(6 × 6)(6 × 6). This is 6 to the tenth power, or 610.



Roots

On the civil service exam, you may be asked to take the square root of a number. This is denoted by a radical sign, which looks like this: . In order to find the square root of a number, try to figure out what number when squared will equal the number under the radical sign. For example, you know that 22 = 4, so 4 = 2. Square roots are easy to calculate for perfect squares. For example 4 = 2, 9 = 3, 16  = 4, 25  = 5, and so forth. Other times you can approximate the value of a radical by pinpointing it between two perfect squares. For example, because 4 = 2 and 9 = 3, 7 must be a number between 2 and 3. In other cases, it is helpful to find equivalents of the radical by applying the rules governing the manipulation of radicals. These rules can be summarized as: ■

■

ab  = a × b This rule is helpful when simplifying 12 , for example. 12  = 4 × 3 = 4 × 3 = 23 a b = a ÷ b 1 This rule is helpful when finding the equivalent of a radical like  2 5 . First take the radical of the top and 1 1 bottom:  . Because 1 = 1 and 25  = 5, you have 1 ÷ 25  = 1 ÷ 5. 2 5 =  25 

Once you are able to convert the radicals into equivalents that have the same number under the radical, you can combine them effectively through addition and subtraction. For example, 22 + 32 = 52 and 53 – 43 = 13.

31

–ARITHMETIC, POWERS, AND ROOTS–



Practice Questions

6. What is the product of 450 and 122? a. 54,900 b. 6588 c. 572 d. 328

1. Find the sum of 7,805 and 987. a. 17,675 b. 8,972 c. 8,987 d. 8,792

7. Find the quotient of 12,440 and 40. a. 497,600 b. 12,480 c. 12,400 d. 311

2. Lawrence gave $281 to Joel. If he originally had $1,375, how much money does he have left? a. $1,656 b. $1,294 c. $1,094 d. $984

8. What is the product of 523 and 13 when rounded to the nearest hundred? a. 6,799 b. 536 c. 6,800 d. 500

3. Peter had $10,573 in his savings account. He then deposited $2,900 and $317. How much is in the account now? a. $13,156 b. $13,790 c. $7,356 d. $6,006

9. When the sum of 1,352 and 731 is subtracted from 5,000, the result is a. 7,083 b. 2,917 c. 2,083 d. 4,379

4. What is the positive difference between 10,752 and 675? a. 11,427 b. 10,077 c. 3,822 d. –10,077

10. What is the quotient of 90 divided by 18? a. 5 b. 6 c. 72 d. 1,620

5. 287,500 – 52,988 + 6,808 = a. 347,396 b. 46,467 c. 333,680 d. 241,320

11. What is the product of 52 and 22? a. 30 b. 74 c. 104 d. 1,144

32

–ARITHMETIC, POWERS, AND ROOTS–

12. What is the sum of the product of 3 and 2 and the product of 4 and 5? a. 14 b. 26 c. 45 d. 90

18. Which of the following demonstrates the commutative property? a. 2 + 3 = 4 + 1 b. 2 + (3 + 4) = (2 + 3) + 4 c. 2 × 3 = 3 × 2 d. 2 × (3 × 4) = (2 × 3) × 4

13. Find the difference of 582 and 73. a. 42,486 b. 655 c. 509 d. 408

19. Which of the following demonstrates the associative property? a. 4 + 5 = 5 + 4 b. 2 × (3 + 4) = (2 × 3) + 4 c. 4 × 5 = 5 × 4 d. 2 × (3 × 4) = (2 × 3) × 4

14. How much greater is the sum of 523 and 65 than the product of 25 and 18? a. 138 b. 545 c. 588 d. 33,545

20. Which of the following demonstrates the distributive property? a. (4 × 5) + 1 = 4 × (5 + 1) b. 4 × (5 + 1) = 4 × 5 + 4 × 1 c. 4 × 5 × 1 = 1 × 5 × 4 d. (4 + 5) + 1 = 4 + (5 + 1)

15. Solve the following: 589 + 7,995 ÷ 15 a. 572 with a remainder of 4 b. 1,122 c. 8,569 d. 8,599

21. 4 × 4 × 4 × 4 is equivalent to a. 4 × 42 b. 42 × 43 c. (42)2 d. 43 + 42

16. 540 ÷ 6 + 3 × 24 = a. 2,232 b. 1,440 c. 1,260 d. 162

22. What is the square root of 81? a. 8 b. 9 c. 10 d. 11

17. 78 × (32 + 12) = a. 2,508 b. 3,432 c. 6,852 d. 29,953

23. 113 = a. 121 b. 1,331 c. 14,641 d. 15,551

33

–ARITHMETIC, POWERS, AND ROOTS–

24. (83)5 = a. 815 b. 88 c. 84 d. 82

30. 1,225 = a. 30 b. 35 c. 40 d. 45

25. 72 = a. 12 b. 63 c. 62 d. 362

31. 3 × 3 × 3 × 3 × 3 × 3 = a. (33)3 b. 32 × 32 × 32 c. 32 × 33 d. (34)2

26. 73 = a. 343 b. 49 c. 38 d. 21

32. 23 + 22 + 53 = a. 43 + 22 b. 42 + 53 c. 82 + 23 d. 73 + 22

27. 2128 = a. 8 2 b. 162 c. 32 2 d. 642

33.

28. 50  + 162 = a. 1062 b. 142 c. 92 d. 52

34. (–3)3 + (3)3 = a. 54 b. 27 c. 0 d. –27

29. 75 – 3(9 – 7)4 = a. 33 b. 1,444 c. 694 d. 54

35. 70  is between which of the following two numbers? a. 5 and 6 b. 6 and 7 c. 7 and 8 d. 8 and 9

1  8 1 =

a. b. c. d.

34

1÷9 1 ÷ 81 1 ÷ 3 1 ÷ 9

–ARITHMETIC, POWERS, AND ROOTS–

36. 183 is how much greater than 162? a. 6,088 b. 5,576 c. 265 d. 68

42. 24 + 27 = a. 228 b. 211 c. 25 d. 23

37. 422 is how much greater than 242? a. 1,188 b. 1,764 c. 576 d. 2,340

43. 32 + 33 = a. 18 b. 27 c. 62 d. 65

2(42 = 38. (–3) ) a. 12 2 b. –122  c. 12 d. –12

44. 711 ÷ 79 = a. 720 b. 7–20 c. 49 d. 1 ÷ 49

39. (–12)2 = a. –144 b. –121 c. 121 d. 144

45. 35 × 32 × 53 × 59 = a. 37 × 512 b. 312 × 57 c. 33 × 56 d. 36 × 53

40. (–3)3 = a. 9 b. –9 c. 27 d. –27

46. (69 × 25) ÷ (68 × 22) = a. 64 b. 48 c. 32 d. 16

41. The square root of 48 is between which two numbers? a. 6 and 7 b. 5 and 6 c. 4 and 5 d. 3 and 4

47.

10 × 1010  5 × 102

a. b. c. d.

35

= 10 × 108 5 × 10–8 2 × 108 5 × 108

–ARITHMETIC, POWERS, AND ROOTS–

48. Find the sum of (3 × 102) and (2 × 105). a. 200,300 b. 23,000 c. 2,300 d. 230

50. A rod that is 8 × 106 mm is how much longer than a rod that is 4 × 104 mm? a. twice as long b. four times as long c. 20 times as long d. 200 times as long

49. What is the product of 2 × 106 and 6 × 107? a. 12 × 1042 b. 12 × 1013 c. 12 × 105 d. 12 × 103

36

–ARITHMETIC, POWERS, AND ROOTS–



Answers 15. b. The rules for the order of operations state that division should be done before addition. Recall PEMDAS: parentheses, exponents, multiplication, division, addition, subtraction. 7,995 ÷ 15 = 533. Next, add: 589 + 533 = 1,122. 16. d. Consider PEMDAS: parentheses, exponents, multiplication, division, addition, subtraction. Here you must solve the division first: 540 ÷ 6 = 90. The equation becomes 90 + 3 × 24. Again, considering PEMDAS, you know you should calculate the multiplication first. 3 × 24 = 72, so the equation reduces to 90 + 72 = 162. 17. b. Remember PEMDAS: parentheses, exponents, multiplication, division, addition, subtraction. Here you must solve the part inside the parentheses first: 32 + 12 = 44. The equation becomes 78 × 44. Multiplying, you get 3,432. 18. c. Note that this question is not looking for a true equation. It is asking which equation represents the commutative property. The commutative property applies for addition and multiplication and can be represented as a + b = b + a or a × b = b × a. Choice c shows this relationship: 2 × 3 = 3 × 2. In other words, the order in which you multiply two numbers does not matter. 19. d. The associative property applies to grouping of addition or multiplication problems. It can be represented as a + (b + c) = (a + b) + c, or a × (b × c) = (a × b) × c. Note that you CANNOT combine addition and multiplication as in choice b. 2 × (3 + 4) ≠ (2 × 3) + 4. Only choice d correctly shows this property: 2 × (3 × 4) = (2 × 3) × 4.

1. d. Sum means addition, so 7,805 + 987 = 8,792. 2. c. To find the difference, subtract: 1,375 – 281 = 1,094. He now has $1,094. 3. b. Add all three values together: 10,573 + 2,900 + 317 = $13,790. 4. b. To find a difference, just subtract. The term positive difference means you are solving for a positive answer. This means you should subtract the smaller number from the larger number: 10,752 – 675 = 10,077. 5. d. 287,500 – 52,988 = 234,512. Next, add: 234,512 + 6,808 = 241,320. 6. a. Product means multiply. 450 × 122 = 54,900. 7. d. A quotient results from division. 12,440 ÷ 40 = 311. 8. c. To find the product, just multiply: 523 × 13 = 6,799. Rounding to the nearest hundred yields 6,800. 9. b. The sum of 1,352 and 731 is obtained by adding: 1,352 + 731 = 2,083. Next you subtract this value from 5,000: 5,000 – 2,083 = 2,917. 10. a. 90 divided by 18 equals 5. Thus, the quotient is 5. 11. d. The product is obtained by multiplying: 52 × 22 = 1,144. 12. b. First, find the two products: 3 × 2 = 6 and 4 × 5 = 20. Next, add these two products together: 6 + 20 = 26. 13. c. To find a difference, you subtract: 582 – 73 = 509. 14. a. First, calculate the two equations: The sum of 523 and 65: 523 + 65 = 588 The product of 25 and 18: 25 × 18 = 450 Next, find the difference: 588 – 450 = 138

37

–ARITHMETIC, POWERS, AND ROOTS–

20. b. The distributive property applies to multiplication over addition such as in choice b: 4 × (5 + 1) = 4 × 5 + 4 × 1. Notice that multiplying the sum of the two terms by 4 is equivalent to multiplying each term by 4 and then adding these values. 21. c. 4 × 4 × 4 × 4 is the same as 44. Choice c also equals 44 because when you raise a power to another power, you simply multiply the exponents. Thus, (42) 2 = 42 + 2. Choice a equals 43, choice b equals 45, and choice d equals 64 + 16, or 80. 22. c. The square root of 81 simply means 81 . To solve, just ask yourself “What number squared equals 81?” 92 = 81, so 81  = 9. 3 23. b. 11 = 11 × 11 × 11 = 121 × 11 = 1,331. 24. a. When raising a power of a base to another power, you just multiply the exponents. Here (83)5 = 83 × 5 = 815. 25. c. 72  = 36 . × 2 Because 36 = 62, you can pull a 6 out from under the radical. Thus, you have 62. 26. a. 73 = 7 × 7 × 7, which equals 49 × 7 = 343. 27. b. 2128  is equal to 64 , × 2 or 2 × 64 × 2. Since 64  = 8, you have 2 × 8 × 2 = 162. 28. b. Each radical can be rewritten. First, 50 = 2 × 25 = 2 × 25  = 2 × 5 = 52. Next, 162  = 81  × 2 = 81  × 2 = 92. Finally, add the two radicals: 52 + 92 = 142. 29. a. To solve, use PEMDAS: parentheses, exponents, multiplication, division, addition, subtraction. First, calculate the value inside the parentheses: 75 – 3(9 – 7)4 = 75 – 3(2)4. Second, calculate the exponent 75 – 3(2)4 = 75 – 3(16). Third, calculate the multiplication: 75 – 3(16) = 75 – 48. Finally, subtract: 75 – 48 = 27. Because 27

30.

31.

32.

33. 34.

35.

36.

37.

38.

38

is not listed as an answer choice, figure out which choice equals 27. Here, choice a, 33 = 3 × 3 × 3 = 27. b. In this case, it is easiest to see which answer choice when squared equals 1,225. Choice a, 30, would yield 30 × 30 = 900, and is thus too small. Choice b, 35, yields 35 × 35 = 1,225. Thus, 1,225  = 35 and choice b is correct. b. 3 × 3 × 3 × 3 × 3 × 3 is equivalent to 36. Choice b is equivalent to 36 because 32 × 32 × 32 equals 32 + 2 + 2. Remember to add the powers when multiplying numbers with the same base. Choice a equals 39, choice c equals 35, and choice d equals 38. d. You can combine the two terms with the 3. 23 + 53 = 73, so the entire expression equals 73 + 22. 1 a.   ÷ 81  = 1 ÷ 9, choice a. 8 1 = 1 c. Cubing a negative number (or taking any odd power of a negative number, for that matter) results in a negative value. Here, –33 = –3 × –3 × –3 = –27. 33 = 27. Thus, the sum (–3)3 + (3)3 = –27 + 27 = 0. d. 82 is 64 and 92 is 81. Thus, the square root of 70 (which is between 64 and 81) must be between 8 and 9. b. First, calculate both quantities: 183 = 18 × 18 × 18 = 5,832 and 162 = 16 × 16 = 256. Next, in order to find out how much greater the first quantity is, you find the difference (by subtracting): 5,832 – 256 = 5,576. a. Calculate both of the given quantities: 422 = 1,764 and 242 = 576. Next, subtract to obtain the difference: 1,764 – 576 = 1,188. 2(42 you will first simplify the c. To solve (–3) ) value under the radical. –32 = 9 and 42 = 16, 2(42 = 9 so (–3) ) . × 16 This can be rewritten as 9 × 16  and simplified to 3 × 4, which equals 12.

–ARITHMETIC, POWERS, AND ROOTS–

10 × 10 10 10 10 – 2 = 2 × 108.     47. c.  5 × 102 = 5 × 102 = 2 × 10 Remember that according to the rules of exponents, when dividing, you can simply subtract the exponents of the two powers of 10. 48. a. 3 × 102 = 3 × 100 = 300 and 2 × 105 = 2 × 100,000 = 200,000. Adding these 2 values yields 200,000 + 300 = 200,300. 49. b. The product of 2 × 106 and 6 × 107 would be 2 × 106 × 6 × 107 = 2 × 6 × 106 × 107. Applying the rules of exponents, you can simply add the exponents of the 2 powers of 10. Thus, 2 × 6 × 106 × 107 = 2 × 6 × 106 + 7 = 2 × 6 × 1013. Multiplying the first 2 terms yields 12 × 1013. 50. d. 8 × 106 mm = 8 × 1,000,000 = 8,000,000 mm. 4 × 104 mm = 4 × 10,000 = 40,000. How many times larger is 8,000,000 than 40,000? 8,000,000 ÷ 40,000 = 200. Thus, the first rod is 200 times longer than the second. 10

39. d. When you square a negative number (or raise a negative number to any even power), the result is a positive number. So, (–12)2 = 144. 40. d. When you raise a negative number to any odd power, the result is a negative number. So, (–3)3= –3  –3  –3 = –27. 41. a. 62 = 36 and 72 = 49. So 48  (which is between 36 and 49) will equal a number that is between 6 and 7. 42. b. Since the base (2) is the same, you can simply add the exponents. 24 × 27 = 24 + 7 = 211. 43. c. 32 = 9 and 33 = 27; 9 + 27 = 36. Because 36 is not listed as an answer choice, calculate which choice equals 36. Here, choice c, 62 = 6 × 6 = 36, and is correct. 44. c. Because the base (7) is the same, you can simply subtract the exponents. 711 ÷ 79 = 711 – 9 = 72 = 49. 45. a. You can apply the rules of exponents to the terms that have the same bases. Thus, 35 × 32 × 53 × 59 = 35 + 2 × 53 + 9 = 37 × 512. 46. b. You can apply the rules of exponents to the terms that have the same bases. Thus, (69 × 25) ÷ (68 × 22) is equivalent to 69 – 8 × 25 – 2 = 61 × 23 = 6 × 8 = 48.

39

10

C H A P T E R

4

Fractions and Decimals

O

n the civil service exam, the problems involving fractions you’ll encounter may be straightforward calculation questions, or they may be word problems. Typically, they ask you to add, subtract, multiply, divide, or compare fractions. part numerator   A fraction is a part of something (a whole). Fractions are written as  whole , or more technically as denominator . Look at three kinds of fractions: Proper fraction: 1 2 4 8 ; ; ; 1 2 3 9 3 The numerator is less than the denominator. The value of a proper fraction is less than 1. Improper fraction: 3 5 14 12 ; ; ;  2 3 9 12 The numerator is greater than or equal to the denominator. The value of an improper fraction is 1 or more.

41

–FRACTIONS AND DECIMALS–

Mixed number: 312; 423; 1234; 2434 A fraction is written to the right of a whole number. The value of a mixed number is more than 1; it is the sum of the whole number plus the fraction.



Changing Improper Fractions into Mixed or Whole Numbers

To change an improper fraction, say 123 , into a mixed number, follow these steps: 1. Divide the denominator (2) into the numerator (13) to get the whole number portion (6) of the mixed number: 2. Write the remainder of the division (1) over the old denominator (2): 3. Check: Change the mixed number back into an improper fraction (see steps in the next section).



13 ÷ 2 = 6 r1. 612

Changing Mixed Numbers into Improper Fractions

It’s easier to multiply and divide fractions when you’re working with improper fractions rather than mixed numbers. To change a mixed number, say 234, into an improper fraction, follow these steps: 1. 2. 3. 4.



Multiply the whole number (2) by the denominator (4): Add the result (8) to the numerator (3): Put the total (11) over the denominator (4): Check: Reverse the process by changing the improper fraction into a mixed number. If you get back the number you started with, your answer is right.

2×4=8 8 + 3 = 11 11  4

Reducing Fractions

50 Reducing a fraction means writing it in lowest terms, that is, with smaller numbers. For instance, 50¢ is  10 0 of a 1 dollar, or 2 of a dollar. In fact, if you have a 50¢ piece in your pocket, you say that you have a half dollar. Reducing a fraction does not change its value. Follow these steps to reduce a fraction:

42

Shortcut—Zeros and Reducing When the numerator and denominator both end in zeros, cross out the same number of zeros in both numbers to begin the reducing process. For example,

3 00  4,0 00

reduces to

3   40

when you cross out two zeros in both

numbers.

1. Find a whole number that divides evenly into both the numerator and the denomination. 2. Divide that number into the numerator, and replace the numerator with the quotient (the answer you got when you divided). 3. Do the same thing to the denominator. 4. Repeat the first three steps until you can’t find a number that divides evenly into both the numerator and the denominator. 8÷4 2 2÷2 1    For example, let’s reduce 284 . You could do it in two steps:  24 ÷ 4 = 6; then  6 ÷ 2 = 3 . Or you could do it in a 8÷8 1  single step:  24 ÷ 8 = 3. Whenever you do arithmetic with fractions, reduce your answer. On a multiple-choice test, don’t panic if your answer isn’t listed. Try to reduce it and then compare it to the choices.



Raising Fractions to Higher Terms

Before you can add and subtract fractions, you have to know how to raise a fraction to higher terms. This is actually the opposite of reducing a fraction. Follow these steps to raise 23 to 24ths: 1. 2. 3. 4.



Divide the old bottom number (3) into the new one (24): Multiply the answer (8) by the old top number (2): Put the answer (16) over the new bottom number (24): Check your answer by reducing the new fraction to see if you get back the original one:

324 =8 2 × 8 = 16 16 2 4 16 ÷ 8  24 ÷ 8

= 23

Adding Fractions

It’s important to remember that when adding or subtracting fractions, you always need them to have the same denominator. Then, whenever you subtract or add, you only need to perform the operation on the numerators, and keep the same denominator.

43

–FRACTIONS AND DECIMALS–

If the fractions have the same denominators, add the numerators together and write the total over the denominator. 2+4 6   Examples: 29 + 49 =  9 = 9 Reduce the fraction: 23 5  8

+ 78 = 182

Change the sum to a mixed number: 148; then reduce: 112 There are a few extra steps to add mixed numbers with the same denominators, say 235 + 145:

2. Change the improper fraction into a mixed number:

3  5 7  5

3. Add the whole numbers:

2+1=3

4. Add the results of steps 2 and 3:

125 + 3 = 425

1. Add the fractions:



+ 45 = 75 = 125

Finding a Common Denominator

If the fractions you want to add don’t have the same denominator, you’ll have to raise some or all of the fractions to higher terms so that they all have the same denominator, the common denominator. See if all the denominators divide evenly into the biggest denominator. If this fails, check out the multiplication table of the largest denominator until you find a number into which all the other denominators evenly divide. When all else fails, multiply all the denominators together. Example: 23 + 45 1. Find the common denominator. Multiply the denominators:

3 × 5 = 15

2. Raise each fraction to 15ths:

2  = 3 4  = 5 22  15

3. Add as usual:



10  15 12  15

Finding the Least Common Denominator

If you are asked to find the least common denominator (LCD), you will need to find the smallest number that is a multiple of the original denominators present. Sometimes you can figure this out mentally, or you will stumble onto the LCD by following the previous steps. However, to be sure that you have the least common denominator, you can use one of two methods:

44

–FRACTIONS AND DECIMALS–

1. Find the least common multiple. This can be done by checking out the multiplication table of the largest denominator until you find a number that all the other denominators evenly divide into, as described previously. 2. Determine the prime factorization of each of the denominators. The least common denominator will encompass every denominator’s prime factorization. Prime numbers are numbers that have only two factors, the number 1 and itself. For example, 3 is prime because its only factors are 1 and 3. 1 is not a prime number. Also, 2 is the only even prime number. Numbers that are not prime can be expressed in terms of prime factors. For example, let’s determine the prime factorization of 12. 12 = 3 × 4 = 3 × 2 × 2 The prime factorization of 12 is 3 × 2 × 2. In order to find the LCD of 34 and 56, you can use the prime factorization method as follows: 1. Find the prime factorization of both denominators: 2. The LCD will contain the prime factorization of both denominators:

4=2×2 6=2×3 4 = 2 × 2 (the LCD must have two 2s.) 6 = 2 × 3 (the LCD must have a 2 and a 3.)

The LCD will be 2 × 2 × 3. Note that this LCD contains the prime factorization of 4 and 6.



Subtracting Fractions

If the fractions have the same denominators, subtract the numerators and write the difference over the denominator. 4–3

Example: 49 – 39 = 9 = 19 If the fractions you want to subtract don’t have the same denominator, you’ll have to raise some or all of the fractions to higher terms so that they all have the same denominator, or LCD. If you forgot how to find the LCD, just read the section on adding fractions with different denominators. Example: 56 – 34 1. Raise each fraction to 12ths because 12 is the LCD, the smallest number that both 6 and 4 divide into evenly: 2. Subtract as usual:

5 10  =  6 12 1 1 2

3  4

= 192

Subtracting mixed numbers with the same denominator is similar to adding mixed numbers.

45

–FRACTIONS AND DECIMALS–

Example: 435 – 125 3  5

– 25 = 15 4–1=3 1 1  + 3 = 3 5 5

1. Subtract the fractions: 2. Subtract the whole numbers: 3. Add the results of steps 1 and 2:

Sometimes there is an extra “borrowing” step when you subtract mixed numbers with the same denominators, say 735 – 245: 1. You can’t subtract the fractions the way they are because 45 is bigger than 35. So you borrow 1 from the 7, making it 6, and change that 1 to 55 because 735 = 655 + 35

5 is the bottom number: 2. Add the numbers from step 1:

655 + 35 = 685

3. Now you have a different version of the original problem:

685 – 245

4. Subtract the fractional parts of the two mixed numbers:

8  5

5. Subtract the whole number parts of the two mixed numbers:

6–2=4

6. Add the results of the last two steps together:

4 + 45 = 445



– 45 = 45

Multiplying Fractions

Multiplying fractions is actually easier than adding them. All you do is multiply the numerators and then multiply the denominators. 2×5 10   For example, 23 × 57 =  3 × 7 = 21

Sometimes you can cancel before multiplying. Cancelling is a shortcut that makes the multiplication go faster because you’re multiplying with smaller numbers. It’s very similar to reducing: if there is a number that divides evenly into a numerator and denominator, do that division before multiplying. If you forget to cancel, you’ll still get the right answer, but you’ll have to reduce it. Example: 56 × 290 1. Cancel the 6 and the 9 by dividing 3 into both of them: 6 ÷ 3 = 2 and 9 ÷ 3 = 3. Cross out the 6 and the 9: 5  6 2

3

× 290

46

Shortcut—The Word Of When you find a fraction of a number, you just find the product of the two numbers. For example, 12 of 10 could be written 12 × 110. This becomes 120, or 5.

2. Cancel the 5 and the 20 by dividing 5 into both of them: 5 ÷ 5 = 1 and 20 ÷ 5 = 4. Cross out the 5 and the 20: 1

5 2

3 ×  2 0 4

3. Multiply across the new numerators and the new denominators: 1×3  2×4

= 38

To multiply a fraction by a whole number, first rewrite the whole number as a fraction with a denominator of 1: Example: 5 × 23 = 51 × 23 = 130 (Optional: convert 130 to a mixed number: 313) To multiply with mixed numbers, it’s easier to change them to improper fractions before multiplying. Example: 423 × 512 1. 2. 3. 4.



Convert 423 to an improper fraction: Convert 512 to an improper fraction: Cancel and multiply the fractions: Optional: convert the improper fraction to a mixed number:

4×3+2

423 = 3 = 134 5×2+1 11  =  512 =  2 2 14 11 77  ×  =  3 2 3 77 2  = 25 3 3

Dividing Fractions

To divide one fraction by a second fraction, invert the second fraction (that is, flip the numerator and denominator) and then multiply. That’s all there is to it! Example: 12 ÷ 35 1. Invert the second fraction 2. Change the division sign (÷) to a multiplication sign (× or • ) 3. Multiply the first fraction by the new second fraction:

47

(35): 53 1  2

1×5 5   × 53 =  2×3 = 6

–FRACTIONS AND DECIMALS–

To divide a fraction by a whole number, first change the whole number to a fraction by putting it over 1. Then, follow the division steps given. 3 3×1   Example: 35 ÷ 2 = 35 ÷ 21 = 35 × 12 =  5 × 2 = 10

When the division problem has a mixed number, convert it to an improper fraction and then divide as usual. Example: 234 ÷ 16 2×4+3 11  =  234 =  4 4 11 1 11 6  ÷  =  ×  4 6 4 1

1. Convert 234 to an improper fraction: 2. Divide 141 by 16 : 3. Flip 16 to 61, change ÷ to ×, cancel and multiply: 11  4 2



3

× 61 = 323

What’s a Decimal?

A decimal is a special kind of fraction. You use decimals every day when you deal with money—for example, $10.35 is a decimal that represents ten dollars and 35 cents. The decimal point separates the dollars from the cents. 1  of a dollar, or $0.01. Because there are 100 cents in one dollar, 1¢ is  100 Each decimal digit to the right of the decimal point has a name: .1 = 1 tenth = 110 2  .02 = 2 hundredths =  100 3 .003 = 3 thousandths =  1,0 00 4  .0004 = 4 ten-thousandths =  10,000 When you add zeros after the rightmost number, you don’t change the value of the decimal. For example, 6.17 is the same as all of these: 6.170 6.1700 6.17000000000000000 If there are digits on both sides of the decimal point (like 10.35), the number is called a mixed decimal. If there are digits only to the right of the decimal point (like .53), the number is called a decimal. A whole number (like 15) is understood to have a decimal point at its right. Thus, 15 is the same as 15.0, 15.00, 15.000, and so on.

48

–FRACTIONS AND DECIMALS–



Changing Fractions to Decimals

To change a fraction to a decimal, divide the denominator into the numerator. You will need to put a decimal point and a few zeros on the right side of the numerator. When you divide, bring the decimal point up into your answer. Example: Change 34 to a decimal. 1. Add a decimal point and two zeros to the top number (3): 3.00 2. Divide the bottom number (4) into 3.00: 0.75 (Be sure to bring the decimal point up into the answer.) The quotient (result of the division) is the answer: 0.75. Some fractions may require you to add many decimal zeros in order for the division to come out evenly. In fact, when you convert a fraction like 23 to a decimal, you can keep adding decimal zeros to the numerator forever because the division will never come out evenly. As you divide 3 into 2, you’ll keep getting 6’s: 2 ÷ 3 = 0.6666666666 . . . This is called a repeating decimal and it can be written as .666. You can approximate it as .67, .667, .6667, and so on.



Changing Decimals to Fractions

To change a decimal to a fraction, write the digits of the decimal as the numerator of a fraction, and write the decimal’s name as the denominator of the fraction. Then, reduce the fraction, if possible. Example: 0.018 1. Write 18 as the top of the fraction: 18 18 2. Three places to the right of the decimal means thousandths, so write 1,000 as the bottom number:  1,0 00 18 ÷ 2 9    3. Reduce the numerator and denominator by dividing by 2:  = 1,000 ÷ 2 500



Comparing Decimals

Because decimals are easier to compare when they have the same number of digits after the decimal point,tack zeros onto the end of the shorter decimals. Then all you have to do is compare the numbers as if the decimal points weren’t there: Example: Compare 0.08 and 0.1 1. Tack one zero at the end of .01 to get 0.10. 2. To compare 0.10 to 0.08, just compare 10 to 8. 3. Since 10 is larger than 8, 0.1 is larger than 0.08.

49

–FRACTIONS AND DECIMALS–



Adding and Subtracting Decimals

To add or subtract decimals, line them up so their decimal points are even. You may want to tack on zeros at the end of shorter decimals so you can keep all your digits lined up evenly. Remember, if a number doesn’t have a decimal point, then put one at the right end of the number. Examples: 1.23 + 57 + 0.038 = 1. Line up the numbers like this:

1.230 57.000 + .038 58.268

2. Add the columns: 1.23 – .038 = 1. Line up the numbers by decimal point:

1.230 – 0.038 2. Subtract the bottom number in each column from the top: 1.192



Multiplying Decimals

To multiply decimals, ignore the decimal points and multiply the numbers. Then count the total number of decimal digits (the digits to the right of the decimal point) in the numbers you’re multiplying. Count off that number of digits in your answer beginning at the right side and put the decimal point to the left of those digits. Example: 215.7 × 2.4 = 1. Multiply 2,157 times 24:

2,157 × 24 51,768 2. Because there are a total of 2 decimal digits in 215.7 and 2.4, count off two places from the right in 51,768, placing the decimal point to the left of the last two digits: 517.68 If your answer doesn’t have enough digits, tack zeros on to the left of the answer. Example: 0.03 × 0.006 = 1. Multiply 3 times 6: 3 × 6 = 18 2. You need five decimal digits in your answer, so tack on three zeros: 00018 3. Put the decimal point at the front of the number (which is five digits in from the right): 0.00018

50

–FRACTIONS AND DECIMALS–



Dividing Decimals

To divide a decimal (.256) by a whole number (8), set up the division (8.2 56 ) and immediately bring the decimal point straight up into the answer (8). Then divide as you would normally divide whole numbers: Example: 0.032 8.2 56  – 24 16 To divide any decimal by a decimal, there is an extra step to perform before you can divide. Move the decimal point to the very right of the number you’re dividing by, counting the number of places you’re moving it. Then, inside the long division sign, move the decimal point the same number of places to the right in the number you’re dividing into. In other words, first change the problem to one in which you’re dividing by a whole number. Example: 0.061. 21 8 1. Because there are two decimal digits in 0.06, move the decimal point two places to the right in both numbers and move the decimal point straight up into the answer: 06.12 1. 8 2. Divide using the new numbers: 20.3 06.12 1. 8 – 12 01 –0 18 – 18 0 Under the following conditions, you have to tack on zeros to the right of the last decimal digit in the number you’re dividing into: ■ ■ ■

if there aren’t enough digits for you to move the decimal point to the right if the answer doesn’t come out evenly when you do the division if you’re dividing a whole number by a decimal

51

–FRACTIONS AND DECIMALS–



Practice Questions

6. What is 3.133 when rounded to the nearest tenth? a. 3 b. 3.1 c. 3.2 d. 3.13

1. Which of the following choices has a 6 in the tenths place? a. 60.17 b. 76.01 c. 1.67 d. 7.061

7.

3 2 0 is equivalent to which of the following decimals?

a. b. c. d.

2. Which of the following choices has a 3 in the hundredths place? a. 354.01 b. 0.54031 c. 0.54301 d. 0.03514

0.03 0.06 0.60 0.15

8. Which number sentence is true? a. 0.23 ≥ 2.3 b. 0.023 ≤ 0.23 c. 0.023 ≤ 0.0023 d. 0.023 ≥ 2.3

3. 234.816 when rounded to the nearest hundredth is a. 200 b. 234.8 c. 234.81 d. 234.82

9. Which decimal is the smallest? a. 0.00782 b. 0.00278 c. 0.2780 d. 0.000782

4. Which of these decimals has the greatest value? a. 0.03 b. 0.003 c. 0.031 d. 0.0031

10. Which decimal is equivalent to the fraction 275 ? a. 0.07 b. 0.35 c. 0.28 d. 0.725

5. 25.682 rounded to the nearest tenth is a. 26 b. 25 c. 25.68 d. 25.7

11. What is the sum of 8.514 and 4.821? a. 12.335 b. 13.335 c. 12.235 d. 13.235

52

–FRACTIONS AND DECIMALS–

12. What is the sum of 2.523 and 6.76014? a. 9.3 b. 92.8314 c. 9.28314 d. 928.314

18. What is the sum of 12.05, 252.11, 7.626, 240, and 8.003? a. 5,197.86 b. 519.789 c. 518.685 d. 518.786

13. 67.104 + 51.406 = a. 11.851 b. 1,185.1 c. 118.51 d. 118.61

19. What is the sum of –8.3 and 9? a. 17.3 b. 0.7 c. 1.73 d. –17.3

14. What is the sum of 3.75, 12.05, and 4.2? a. 20 b. 19.95 c. 19.00 d. 19.75

20. The following is a list of the thickness of four boards: 0.52 inches, 0.81 inches, 0.72 inches, and 2.03 inches. If all four boards are stacked on top of one another, what will the total thickness be? a. 40.8 inches b. 0.408 inches c. 4.008 inches d. 4.08 inches

15. 14.02 + 0.987 + 0.145 = a. 14.152 b. 15.152 c. 14.142 d. 15.142

21. 324.0073 – 87.663 = a. 411.6703 b. 236.3443 c. 236.3443 d. 23.634443

16. 5.25 + 15.007 + 0.87436 = a. 211.3136 b. 20.13136 c. 201.3136 d. 21.13136 17.

22. 8.3 – 1.725 = a. 6.575 b. 6.775 c. 7.575 d. 10.025

1  5

+ 0.25 + 18 + 0.409 = a. 113 + 0.659 b. 0.659 + 410 c. 0.984 d. 1.084

23. 12.125 – 3.44 = a. 9.685 b. 8.785 c. 8.685 d. 8.585

53

–FRACTIONS AND DECIMALS–

24. 89.037 – 27.0002 – 4.02 = a. 62.0368 b. 59.0168 c. 58. 168 d. 58.0168

30. –6.5 – 8.32 = a. 14.82 b. 1.82 c. –0.82 d. –14.82

25. 0.89735 – 0.20002 – 0.11733 = a. 0.69733 b. 0.59733 c. 0.58033 d. 0.58

31. 0.205 × 0.11 = a. 0.02255 b. 0.2255 c. 2.255 d. 22.55

26. What is 287.78 – 0.782 when rounded to the nearest hundred? a. 286.998 b. 286.90 c. 286.99 d. 300

32. 0.88 × 0.22 = a. 0.01936 b. 0.1936 c. 0.1616 d. 1.616 33. 8.03 × 3.2 = a. 24.06 b. 24.6 c. 25.696 d. 156.96

27. 0.0325 – (–0.0235) = a. 0 b. 0.0560 c. 0.0650 d. 0.560

34. 0.56 × 0.03 = a. 168 b. 16.8 c. 0.168 d. 0.0168

28. 0.667 – (–0.02) – 0.069 = a. 0.618 b. 0.669 c. 0.596 d. 0.06

35. 0.32 × 0.04= a. 0.128 b. 0.0128 c. 128 d. 12.8

29. –12.3 – (–4.2) = a. –8.1 b. –16.5 c. 16.5 d. 8.1

54

–FRACTIONS AND DECIMALS–

36. What is the product of 5.49 and 0.02? a. 0.1098 b. 5.51 c. 5.47 d. 274.5

41. 3.26 ÷ 0.02 = a. 163 b. 65.2 c. 16.3 d. 652

37. 0.125 × 0.8 × 0.32 =

42. 512 ÷ 0.256 = a. 20 b. 2,000 c. 200 d. 2

a. 0.32 b. c. d.

1 1 0 8   250 32  10 0

43. 3.4 ÷ 0.17 = a. 3 b. 2 c. 30 d. 20

1  5

38. 0.15 × = a. 0.2 b. 0.3 c. 0.02 d. 0.03

44. What is the quotient of 83.4 ÷ 2.1 when rounded to the nearest tenth? a. 40 b. 39.71 c. 39.7 d. 39.8

39. If each capsule contains 0.03 grams of active ingredients, how many grams of active ingredients are in 380 capsules? a. 12623 grams b. 11.4 grams c. 12.6 grams d. 1.14 grams

45. 0.895 ÷ 0.005 = a. 0.0079 b. 0.179 c. 179 d. 1,790

40. If a piece of foil is 0.032 centimeters thick, how thick would a stack of 200 pieces of foil be? a. 64 centimeters b. 16 centimeters c. 6.4 centimeters d. 1.6 centimeters

46. What is the quotient of 0.962 ÷ 0.023 when rounded to the nearest hundredth? a. 41.83 b. 41.826 c. 40 d. 41.82

55

–FRACTIONS AND DECIMALS–

47.

8.4  .09

a. b. c. d. 48.

49. A 70-pound bag of cement can be divided into how many smaller bags, each weighing 3.5 pounds? a. 20 b. 16 c. 10 d. 5

= 9313 0.0107 0.756 75.6

375  .12 5

a. b. c. d.

= 5,625 3,000 56.25 30

50. Markers will be placed along a roadway at 0.31 kilometer intervals. If the entire roadway is 1.55 kilometers, how many markers will be used? a. 480.5 b. 50 c. 48.05 d. 5

56

–FRACTIONS AND DECIMALS–

Answers

6

units (ones)

tenths

hundredths

thousandths

hundredths

tenths

units (ones)

1.

tens

3. d. When rounding to the nearest hundredth, you need to truncate (cut short) the number, leaving the last digit in the hundredths place. If the number after the hundredths place is a 5 or higher, you would round up.

1. c. The places to the right of the decimal point are (in order): the tenths place, the hundredths place, thousandths place, and so on. You are looking for a 6 in the tenths place, which is the first spot to the right of the decimal point. Only choice c has a 6 in this place:

hundreds



2

3

4.

8

1

6

7

units (ones)

tenths

hundredths

thousandths

ten thousandths

hundred thousandths

Note that choice a has a 6 in the tens place and NOT the tenths place. 2. d. The places to the right of the decimal point are (in order): the tenths place, hundredths place, thousandths place, and so on. You are looking for a 3 in the hundredths place, which is the second spot to the right of the decimal point. Only choice d has a 3 in this place:

0.

0

3

5

1

4

6 is higher than 5, so you round the 1 in the hundredths place up to 2. Thus, the answer is 234.82, choice d. 31 4. c. Choice c has the greatest value,  1,0 00 . Here is a comparison of the four choices:

Note that choice a has a 6 in the hundreds place and NOT the hundredths place.

57

a. .03

3 100

30 = 1,000

b. .003

3 1,000

c. .031

31 1,000

d. .0031

31 10,000

–FRACTIONS AND DECIMALS–

9. d. Each answer choice is equivalent to the following values:

5. d. 25.682 has a 6 in the tenths place. Because the number in the hundredths place (8) is greater than 5, you will round up to 25.7.

782 7,820  a. 0.00782 =  100,0 00 =  1,000 ,000 278 2,780  b. 0.00278 =  100,0 00 =  1,000 ,000

tens

units (ones)

tenths

hundredths

thousandths

2,780 287,000 c. 0.2780 =  10,0 00 =  1,000 ,000

2

5.

6

8

2

782 d. 0.000782 =  1,000 ,000 Thus, choice d is the smallest number listed.

10. c. 275 can be translated into hundredths by mul28 tiplying by 44. Thus, 275 × 44 =  10 0 . 28 hundredths can be rewritten as 0.28, choice c. 11. b. Sum means add. Make sure you line up the decimal points and then add: 8.514 + 4.821 13.335 12. c. Sum means add. Line up the decimal points and add: 2.523 + 6.76014 9.28314 13. c. Line up the decimal points and add: 67.104 + 51.406 118.51 14. a. 4.2 is equivalent to 4.20. Line up all the decimal points and add: 3.75 12.05 + 4.20 20.00 15. b. 14.02 is equivalent to 14.020. Line up all the decimal points and add: 14.020 .987 + .145 15.152 16. d. Add zeros as space holders to the numbers 5.25 and 15.007. Then, line all the numbers

1

3

thousandths

tenths

3.

hundredths

units (ones)

You round up because 8 ≥ 5. 6. b. In order to round to the nearest tenth, you need to cut the number short, leaving the last digit in the tenths place. Here you cut the number short without rounding up because the number in the hundredths place is not ≥ 5.

3

You don’t round up because 3 is less than 5. Thus, the answer is 3.1, choice b. 7. d. 230 can quickly be converted to hundredths by 15 15 multiplying by 55: 230 × 55 =  10 0;  10 0 is the same as 15 hundredths, or 0.15, choice d. 23 8. b. 0.023 equals  1,0 00 , which is less than 0.23, 23 which equals  10 0 . Thus 0.023 ≤ 0.23. The symbol “≤” means less than or equal to.

58

–FRACTIONS AND DECIMALS–

17.

18.

19.

20.

21. b. Line up the decimal points and subtract: 324.0073 – 87.663 236.3443 22. a. Rewrite 8.3 as its equivalent 8.300. Line up the decimal points and subtract: 8.300 –1.725 6.575 23. c. Line up the decimal points and subtract: 12.125 – 3.44 8.685 24. d. First, rewrite 89.037 as its equivalent 89.0370. Next, subtract 27.0002: 89.0370 – 27.0002 6,2.0368 Now you must subtract 4.02 from the 62.0386. (If you selected choice a, you forgot the next step.) 62.0368 – 4.02 58.0168 25. d. Perform the indicated operations (subtractions) in two steps: 0.89735 – 0.20002 0.69733 Next, subtract 0.11733 from 0.69733 to get 0.58. 26. d. The question asks you to round to the hundred (not hundredth!). 287.78 – 0.782 = 286.998. When this value is rounded to the nearest hundred, you get 300.

up by their decimal points and add: 5.25000 15.00700 + .87436 2,1.13136 c. First convert the fractions to decimals: 15 = .2 and 18 = .125. Next, line up all the numbers by their decimal points and add (note that zeros are added as place holders): 0.200 0.250 0.125 + .409 .984 b. Sum signifies addition. Line up the decimal points and add. Note that zeros can be added as place holders: 12.050 252.110 7.626 240.000 + 8.003 519.7890 b. 9 plus –8.3 is the same as 9 minus 8.3. Rewrite 9 as 9.0 and subtract: 9.0 – 8.3 .7 d. Line up the decimal points and add: 0.52 0.81 0.72 + 2.03 4.08

59

–FRACTIONS AND DECIMALS–

32. b. First, multiply in the usual fashion (ignoring the decimal points): 0.88 × 0.22 = 1,936. Next, you need to insert the decimal point in the correct position, so take note of the position of each decimal point in the two factors:

27. b. Subtracting a negative is the same as adding a positive. Thus, 0.0325 – (– 0.0235) is the same as 0.0325 + 0.0235. Adding, you get 0.0560. 28. a. Subtracting a negative is the same as adding a positive. Thus, 0.667 – (–0.02) – 0.069 = 0.667 + 0.02 – 0.069. This equals 0.687 – 0.069 = 0.618. 29. a. Subtracting a negative number is the same as adding a positive number. Thus, –12.3 – (–4.2) = –12.3 + 4.2; –12.3 and 4.2 will yield a negative value because you are starting 12.3 units away from zero in the negative direction. Adding 4.2 will bring you closer to 0, but you will still have a negative answer. To figure out what the answer is, subtract 4.2 from 12.3 and add a minus sign. Thus, you get –8.1. 30. d. –6.5 – 8.32 is the same as –6.5 + –8.32. When adding two negative numbers, first ignore the negative signs and add in the normal fashion. 6.5 + 8.32 = 14.82. Next, insert the negative sign to get –14.82, choice d. 31. a. First, multiply in the usual fashion (ignoring the decimal points): 0.205 × 0.11 = 2,255. Next, you need to insert the decimal point in the correct position, so take note of the position of each decimal point in the two factors: 0.532

0.88

The decimal point is 2 places to the left.

0.22

The decimal point is 2 places to the left.

In the

The decimal point should be

answer . . . 2 + 2, or 4 places to the left.

1,936 becomes 0.1936, choice b. 33. c. First, multiply in the usual fashion (ignoring the decimal points): 8.03 × 3.2 = 25,696. Next, you need to insert the decimal point in the correct position, so take note of the position of each decimal point in the two factors: 8.03

The decimal point is 2 places to the left.

3.2

The decimal point is 1 place to the left.

In the

The decimal point should

answer . . . 3 places to the left.

25,696 becomes 25.696, choice c. 34. d. Multiply in the usual fashion, and insert the decimal point 4 places to the left:

The decimal point is 3 places to the left.

0.56 0.89

The decimal point is 2 places

The decimal point is 2 places to the left.

to the left. 0.03 In the

The decimal point should be

The decimal point is 2 places to the left.

answer . . . 3 + 2, or 5 places to the left. In the

The decimal point should

answer . . . 4 places to the left.

2,255 becomes .02255, choice a.

0.56 × 0.03 = 168 (when ignoring decimal) and becomes .0168 when you insert the decimal point four places to the left. Thus, the answer is choice d. 60

–FRACTIONS AND DECIMALS–

43. d. The problem 3.4 ÷ 0.17 can be solved with long division. First, move the decimal point two places to the right in each number:

35. b. Multiply in the usual fashion, and insert the decimal point 4 places to the left: 0.32 × 0.04 = 0.0128. 36. a. The term product signifies multiplication. Multiply 5.49 by 0.02 in the usual fashion, and insert the decimal point 4 places to the left: 5.49 × 0.02 = 0.1098. 37. c. First multiply 0.125 by 0.8 to get 0.1. Next multiply 0.1 by 0.32 to get 0.032. This answer 32 is equivalent to 32 thousandths, or  10 0 . This 8 , choice c. reduces to  250 38. d. First convert 15 to a decimal: 15 = 1 ÷ 5 = 0.2. Next multiply: 0.15 × 0.2 = 0.03 39. b. Multiply the amount of active ingredients in one capsule (0.03) by the number of capsules (380): 380 × 0.03 = 11.4 grams. 40. c. To solve, simply multiply the thickness of each piece by the total number of pieces. 200 × 0.032 = 6.4 centimeters. 41. a. The problem 3.26 ÷ .02 can be solved with long division. First, move the decimal point two places to the right in each number:

0 2

1 7

3 4 0

Next, divide as usual to get 20, choice d. 44. c. The problem 83.4 ÷ 2.1 can be solved with long division, moving the decimal point in each number one place to the right:

2 1 8 3 4 Next, divide as usual to get 39.714286. Finally, round to the nearest tenth: 39.7, choice c. 45. c. The problem 895 ÷ 0.005 can be solved with long division, moving the decimal point in each number three places to the right:

0 0 5

8 9 5

Next, divide to get the answer: 179, choice c. 46. a. The problem 0.962 ÷ 0.023 can be solved with long division, moving the decimal point in each number three places to the right:

3 2 6

Next, divide as usual to get 163, choice a. 42. b. The problem 512 ÷ 0.256 can be solved with long division. Move the decimal point three places to the right in each number:

0 2 3

9 6 2

Next, divide to get 41.826087. Rounding this number to the nearest hundredth yields 41.83, choice a. 47. a. The problem 8.4 ÷ 0.09 can be solved with long division, moving the decimal point in each number two places to the right:

2 5 6 5 1 2 0 0 0 Next, divide as usual to get 2,000, choice b.

0 2 3

9 6 2

Dividing yields an answer of 93.333333 . . . or 9313, choice a.

61

–FRACTIONS AND DECIMALS–

50. d. To solve, divide the 1.55 kilometer distance by the interval, 0.31 kilometers. 1.55 ÷ 0.31 can be solved with long division. The decimal point in each number is moved two places to the right:

48. b. The problem 375 ÷ 0.125 can be solved with long division, moving the decimal point in each number three places to the right:

1 2 5 3 7 5 0 0 0

3 1

Dividing yields 3,000, choice b. 49. a. To solve, divide 70 by 3.5. This can be solved with long division, moving the decimal point in each number one place to the right:

1 5 5

Next, divide to get 5, choice d.

3 5 7 0 0 Next, divide as usual to get 20, choice a.

62

C H A P T E R

5

Percents

P

ercents are a way of expressing values out of 100. For example, 30% (30 percent) is equivalent to 30 30 out of 100 or  10 0 . Thus, you can express a percent as a fraction by placing the value before the percent symbol over 100. You can express a percent as a decimal by moving the current decimal point two places to the left. For example, 30% is also equivalent to 0.30. You can convert a decimal value into an equivalent percent by moving the current decimal point two places to the right. For example, 0.30 = 30%. This makes sense because percents are just hundredths, so 0.30 is 30 hun30 dredths, or  10 0 , otherwise known as 30%.

63

–PERCENTS–

Fractions can be converted to percentages by converting to a denominator of 100. This can be done by setting up a simple proportion. For example, to convert 25 into an equivalent percentage, you set up this proportion: 2  5

? = 10 0

Cross multiply to get 2 × 100 = 5 × ?, or 200 = 5 × ?. Divide both sides by 5 to get ? = 40. Thus, 25 is equivalent to 40%.



Taking the Percent of a Number

When you are calculating the percent of a number, just remember that of means multiply. For instance, 50% of 40 is 50% × 40. You can convert 50% to 0.50 and multiply 0.50 × 40 = 20. To save time, you should be familiar with the following equivalencies: FRACTION



PERCENT

1  5

20%

1  4

25%

1  3

approximately 33%

1  2

50%

2  3

approximately 66%

3  4

75%

Unknown Percents

? When you do not know the percent of a value, you can express this percent as  10 0 . This means that when you see ? the phrase what percent, you can express this mathematically as  10 0.

64

–PERCENTS–



Percent Change, Percent Error, and Percent Profit or Loss

When calculating a percent change (such as a percent increase or decrease) you simply express the ratio of the change to the initial as a value over 100. The general proportion to use is: Change  Initial

? = 10 0

Similarly, when calculating the percent error, you set a proportion that equates the difference between the calculated value and the actual value to the actual value with an unknown out of 100: Difference in values  Actual value

? = 10 0

When setting up a proportion to calculate percent profit or loss, you create a ratio of the net profit (or loss) to the initial cost and set this ratio equal to an unknown out of 100: net profit  initial



? = 10 0

net loss  initial

? = 10 0

Simple and Compound Interest

The formula for simple interest is I = PRT. The amount of money deposited is called the principal, P. The interest rate per year is represented by R, and T represents the time in years. When calculating compound interest, it is easiest to sequentially calculate the interest earned using I = PRT. You should be familiar with the following ways of compounding interest: ■ ■ ■ ■ ■

compounded annually: interest is paid each year compounded semiannually: interest is paid two times per year compounded quarterly: interest is paid four times a year compounded monthly: interest is paid every month compounded daily: interest is paid every day

65

–PERCENTS–



6. When expressed as a percent, 3510 is equivalent to

Practice Questions

a. 62% b.

1. 15% is equivalent to which fraction? a.

3 2 0

b.

15  1,000

c.

1  5 1 1 5

d.

c.

d. 31% 7. Another way to write 26.5% is

d.

26.5  1,000

8. 0.0037% is equivalent to which of the following fractions? a. b. c. d.

4. 73% can be expressed as which of the following fractions?

c.

d.

b.

3. When converted to a decimal, 45% is equivalent to a. 0.045 b. 0.45 c. 4.5 d. 45

b.

c.

0.265  100 26  80 53  20 0

a.

2. 20% is equivalent to which decimal value? a. 0.020 b. 2.0 c. 0.2 d. 0.002

a.

31 % 50 3 % 5

37  1,0 00 37  10,0 00 37  1,000 ,000 37   10,000,000

9. Which of the following is 17% of 6,800? a. 115,600 b. 340 c. 578 d. 1,156

0.73  100 73  100 73  1,0 00 0.73  0.10

10. Which number sentence is false? a. 20% ≤ 15

5. 1.5% is equivalent to which decimal value? a. 0.15 b. 1.5 c. 0.0015 d. 0.015

b. 25% = 28 c. 35% > 2540 d.

66

3  4

≤ 80%

–PERCENTS–

11. Express 12 out of 52 to the nearest percent. a. 23% b. 24% c. 25% d. 26%

17. 40% of what number is equal to 460? a. 575 b. 640 c. 860 d. 1,150

12. 45% is equal to a. 80 b. 8 c. 0.08 d. 0.008

18. Larry makes a 12% commission on every car he sells. If he sold $40,000 worth of cars over the course of three months, what was his commission on these sales? a. $44,800 b. $35,200 c. $8,000 d. $4,800

13. 50% of what number equals 20% of 2,000? a. 200 b. 400 c. 600 d. 800

19. USB drives cost $100 each. When more than 50 are purchased, an 8% discount is applied. At a store that charges 8% tax, how much money will 62 USB drives cost? (Round to the nearest cent.) a. $6,200.00 b. $6,160.32 c. $5,704.00 d. $456.32

14. 300% of 54.2 equals a. 16.26 b. 162.6 c. 1,626 d. none of the above 15. What percent of 12 is 18? a. 25% b. 50% c. 80% d. none of the above

20. Aesha made $64,000 in 2007, but she had to pay 26% tax on that amount. How much did she make after taxes? a. $16,640 b. $67,640 c. $47,360 d. $42,360

16. To calculate 75% of a dollar amount, you can a. multiply the amount by 75. b. divide the amount by 75. c. multiply the amount by 34. d. divide the amount by 34.

21. What percent of 89 is 23? a. 33% b. 66% c. 75% d. 133%

67

–PERCENTS–

25. What percent of the square is shaded?

22. 400 books went on sale this week. So far, 120 have been sold. What percent of the books remain? a. 15% b. 30% c. 70% d. 80% 23. What percent of the circle is shaded?

a. b. c. d.

20% 37.5% 40% 80%

26. What percent of the square is shaded? a. b. c. d.

25% 50% 75% 100%

24. What percent of the square is shaded?

a. b. c. d.

a. b. c. d.

20% 37.5% 40% 80%

27. A dealer buys a car from the manufacturer for $13,000. If the dealer wants to earn a profit of 20% based on the cost, at what price should he sell the car? a. $16,250 b. $15,600 c. $15,200 d. $10,833

25% 50% 75% 100%

28. 33 is 12% of which of the following? a. 3,960 b. 396 c. 275 d. 2,750

68

–PERCENTS–

33. At the city park, 32% of the trees are oaks. If there are 400 trees in the park, how many trees are NOT oaks? a. 128 b. 272 c. 278 d. 312

29. Of the numbers listed, which choice is NOT equivalent to the others? a. 52% b. 1235 c. 52 × 10–2 d. 0.052 30. Emily made $8,000 and put half that amount into an account that earned interest at a rate of 6%. After 2 years, what is the dollar amount of the interest earned? (Use the formula I = PRT.) a. $4,800 b. $960 c. $660 d. $480

34. Which ratio best expresses the following: five hours is what percent of a day? a. b. c. d.

31. If Kamil puts $10,000 in the bank at a 6% rate of interest, how much interest will he make in 8 months? (Use the formula I = PRT.) a. $400 b. $350 c. $300 d. $250

5 x   = 2 100 4 5 24 2 4 = x 5 x 2 4 = 10 0 x 24  10 0 = 5

35. If 10% of a number is 45, what would 20% of that number be? a. 9 b. 90 c. 450 d. 900 36. A dozen staplers cost $10.00, and they will then be sold for $2.50 each. What is the rate of profit? a. 75% b. 100% c. 150% d. 200%

32. If Veronica deposits $5,000 in an account with a yearly interest rate of 9%, and leaves the money in the account for 8 years, how much interest will her money earn? a. $360,000 b. 45,000 c. 3,600 d. 450

37. A statue was bought at a price of $50 and sold for $38. What is the percent loss? a. 12% b. 15% c. 24% d. 30%

69

–PERCENTS–

42. $8,000 is deposited into an account. If interest is compounded semiannually at 5% for 1 year, how much money is in the account at the end of the year? a. $8,175 b. $8,200 c. $8,400 d. $8,405

38. The price of a $130 jacket was reduced by 10% and again by 15%. What is the new cost of the jacket? a. $97.50 b. $99.45 c. $117 d. $105 39. At an electronics store, all items are sold at 15% above cost. If the store purchased a printer for $85, how much will they sell it for? a. $90 b. $98.50 c. $97.75 d. $95.50

43. $14,000 is deposited into an account. If interest is compounded quarterly at 8% for 9 months, how much money will be in the account at the end of this period? a. $14,280.00 b. $14,565.60 c. $14,856.91 d. $15,154.05

40. Marla paid $14,105 for her new car. This price included 8.5% for tax. What was the price of the car excluding tax? a. $13,000.00 b. $13,850.00 c. $11,989.25 d. $1,198.93

44. Suki has $1,000 to invest. She would like to invest 53 of it at 6% simple interest. The remainder would be invested at 8% simple interest. How much interest would she have earned after one year? a. $32 b. $36 c. $68 d. $70

41. Steven’s income was $34,000 last year. He must pay $2,380 for income taxes. What is the rate of taxation? a. 70% b. 7% c. 0.7% d. 0.007%

45. How many twelfths are there in 3313%? a. 1 b. 4 c. 33 d 100 46. What is the percent increase from 150 to 200? a. 25% b. 3313% c. 75% d. 6623%

70

–PERCENTS–

49. A five-gallon tank is completely filled with a solution of 50% water and 50% alcohol. Half of the tank is drained and 2 gallons of water are added. How much water is in the resulting mixture? a. 2.5 gallons b. 3.25 gallons c. 3.5 gallons d. 4.5 gallons

47. What is the percent decrease from 200 to 150? a. 25% b. 3313% c. 75% d. 6623% 48. If a crate weighing 600 pounds weighs 540 pounds on a broken scale, what is the percent error? a. 10% b. 11% c. 15% d. 25%

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Answers

15 15 3 1. a. 15 percent equals  10 0.  10 0 reduces to 2 0. 2. c. To change 20% to its equivalent decimal form, move the decimal point two places to the left. Thus, 20% = .20. Choice c, 0.2, is equivalent to 0.20. 3. b. When you see a percent symbol (%), you move the decimal point two places to the left. Thus, 45% is equivalent to 0.45. 4. b. When you see a percent symbol (%), you can rewrite the percent as a fraction by placing the 73 value over 100. Thus, 73% is equivalent to  10 0. 5. d. 1.5% can be converted to its equivalent decimal form by moving its decimal point two places to the left. Thus, 1.5% is equivalent to 0.015, choice d. 6. a. When written as fractions, percents have a denominator of 100. You can convert 5301 to a fraction with a denominator of 100 by multi62 plying by 22; 5301 × 22 =  10 0 = 62%, choice a. 26.5  7. c. First, put 26.5 over 100 =  100 . This is not an answer choice, so you need to reduce. Multi26.5 10 26.5 10     ply  100 by 10 before reducing: 100 × 10 = 265 265 53 . Now you reduce  =  1,000 1,000 20 0. 8. c. To change a percent to a fraction, first put the 0.0037  percent over 100. Thus, 0.0037% =  100 . In order to get a whole number in the numera10,000  tor, multiply the fraction by  10,000 . Thus, 37 0.0037 10,000  ×  =  1,000 ,000 . 100 10,000 9. d. You need to find 17%, or 0.17 of 6800. Remember that of means multiply: 0.17 × 6,800 = 1,156. 20 1 10. c. 20% =  10 0 , or 5, so choice a represents a true 25 1 2 1 statement. 25% =  10 0 = 4, and 8 = 4, so 35 choice b is also true. In choice c, 35% =  10 0 24 48   and 2540 =  . Thus, the statement 35% > 100 5 0 is not true. Choice c is therefore the correct

11.

12. 13.

14. 15.

16.

17.

18. 19.

72

answer. In choice d, 34 = 75%, which is in fact less than 80%. a. “12 out of 52” is written as 1522 . Set up a proportion to see how many hundredths 1522 is ? equivalent to: 1522 =  10 0 . Cross multiplying yields 100 × 12 = 52 × ?, or 1,200 = 52 × ?. Dividing both sides by 52 yields ? = 23.07623. When expressed to the nearest percent, this rounds to 23%. d. It is easier to change 45 into 0.8 before dealing with the percent symbol. 45% = 0.8% = 0.008. d. “50% of what number equals 20% of 2,000?” can be written mathematically as 0.50 × ? = 0.20 × 2,000. Dividing both sides by 0.5 will yield (.2)(2,000)  = 800. ?= .5 300  b. 300% equals  100 , or 3. To find 300% of 54.2, multiply 3 times 54.2: 3 × 54.2 = 162.6. ? a. “What percent” can be expressed as  10 0 . The 1 1 question “What percent of 2 is 8?” can be ? 1 1 expressed as:  10 0 × 2 = 8. This simplifies to ? 1  20 0 = 8. Cross multiplying yields 8 × ? = 200. Dividing both sides by 8 yields 25. 75 3 3 c. 75% =  10 0 . This reduces to 4. Taking 4 of a dollar amount means you multiply the dollar amount by 34. d. The question: “40% of what number is equal to 460?” can be written mathematically as: 0.40 × ? = 460. Next, divide both sides by 0.40 to yield ? = 1,150. d. He gets 12% of $40,000, or 0.12 × $40,000 = $4,800. b. Since more than 50 drives are being purchased, use the discounted price. Take 8% ($8) off the cost of each drive. So, instead of costing $100 each, the drives will be $92 each.

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20.

21.

22.

23. 24. 25.

26.

27.

28.

29.

Next, multiply 62 drives by the price of each drive: 62 × 92 = $5,704. Next, calculate the tax. $5,704 × 0.08 = $456.32. Add the tax to the $5,704 to get $6,160.32. c. The tax on the $64,000 will equal 0.26 × 64,000 = $16,640. Subtract the tax from her earnings: 64,000 – 16,640 = 47,360. c. The question “What percent of 89 is 23?” can be ? 8 2 expressed mathematically as  10 0 × 9 = 3. ? 2 8 Divide both sides by 89 to get  10 0 = 3 ÷ 9 or ? ? ? 2 9 18   10 0 = 3 × 8. This simplifies to  10 0 = 2 4 , or 100 300  = 34. Multiply both sides by 100 to get ? =  4 , so ? = 75. c. 120 out of a total of 400 were sold. Set up a proportion to see what this would be equivalent to when expressed out of 100. ? 120  =  10 0 400 Cross multiplying, you get 120 × 100 = 400 × ?, which is the same as 12,000 = 400 × ?, and dividing both sides by 400 yields ? = 30. Thus 30% were sold, so 70% remain. 50 b. 12 of the circle is shaded. 12 =  10 0 = 50%. 75 3 3 c. 4 of the square is shaded. 4 =  10 0 = 75%. 3 b. 8 of the square is shaded. 3 ÷ 8 = 0.375. To express this as a percent, move the decimal two places to the right: 37.5%. b. 166 of the square is shaded. 166 reduces to 38. 3 ÷ 8 = 0.375. To express this as a percent, move the decimal two places to the right: 37.5%. b. A 20% markup yields a new price that is 120% of the original price. $13,000 × 1.20 = $15,600. c. “33 is 12% of what number” can be expressed mathematically as 33 = 0.12 × ?. Divide 33 by 0.12 (12%) to get 275. d. 52% is the same as 0.52 (drop the % sign and move the decimal point two places to the 52 left). 1235 = 2560 =  10 0 ; 52 ÷ 100 = 0.52. And 52 ×

30.

31.

32.

33.

34.

35.

73

10–2 = 52 × 0.01 = 0.52. Obviously, 0.052 does not equal 0.52, so your answer is d. d. I = PRT means Interest = principal × rate of interest × time. Principal = your original amount of money (in dollars), and time is in years. Be careful; the original amount of money (P) is $4,000 because Emily put 12 of the $8,000 into the account. I = 0.06 and T = 2 years. Substituting into I = PRT, you get I = (4,000)(0.06)(2) = $480. a. Use the formula I = PRT to solve this problem. Here, you were given the timeframe of 8 months, so you need to convert to years. 8 1 yr 8 2 months ×  12 mo nths = 1 2 yr = 3 yr. You are given P = $10,000 and R = 6% or 0.06. Next, you substitute these values into the equation: I = PRT I = ($10,000)(0.06)(23) = 600 × 23 1,200  = 3 = $400 c. In the formula I = PRT, the amount of money deposited is called the principal, P. The interest rate per year is represented by R, and T represents the number of years. The interest rate must be written as a decimal. Here P = 5,000, R = 9% = 0.09, and T = 8. Substitute these numbers for the respective variables and multiply: I = 5,000 × 0.09 × 8 = $3,600. b. First, determine what percent of the trees are not oaks by subtracting. 100% – 32% = 68%. Change 68% to a decimal (0.68) and multiply: 0.68 × 400 = 272. c. The problem can be restated as: 5 hours is to 24 hours as x% is to 100%. This is the same x as 254 =  10 0. b. First figure out what the number is. If 10% of a number is 45, you can call the number “?” and write 0.10 × ? = 45. Divide both sides by

–PERCENTS–

36.

37.

38.

39.

40.

41.

42. d. Because the interest is compounded semiannually (twice a year), after 12 a year the amount of interest earned I = PRT = 8,000 × 0.05 × 12 = $200. Now the account has $8,200 in it. Next, calculate the interest for the second half of the year with I = PRT = 8,200 × 0.05 × 12 = 205. Thus, the answer is $8,405. 43. c. Note that 9 months = 34 of a year. Because interest is compounded quarterly (4 times a year), after 14 of a year, the amount of interest earned will be I = PRT = 14,000 × 0.08 × 14 = $280. The amount in the account after this time will be $14,280. After another 14 of a year, you add I = PRT = 14,280 × .08 × 14 = $285.60. The new total is $14,565.60. After the next 14 of a year, the amount of interest earned is I = PRT = 14565.60 × 0.08 × 14 = $291.312. The amount in the account after 34 of a year is $14,856.91. 44. c. Because Suki is making 2 investments, first find 35 of $1,000. Divide $1,000 into 5 equal 1,000 parts ($5 = $200) and take 3 parts ($600). $600 is invested at 6% simple interest, which yields: $600(6%) = $600(0.06) = $36 The remaining $400 is invested at 8% simple interest, which yields: $400(8%) = $400(0.08) = $32 The total interest earned is $36 + $32 = $68. 45. b. Convert 3313% into a fraction, remembering 1 . that the percent sign is equivalent to  100 1 4 1 100 1 1  = . Now,  = 1 333% = 3 ×  100 2 . There3 3 1 fore, there are 4 twelfths in 333% 46. b. Use the proportion: ? Change  =  10 0 Initial where the change = 200 – 150 = 50, and the initial value is 150. Thus, you have: 50 ?  15 0 = 10 0 Cross multiply to get 50 × 100 = 150 × ?, or

0.10 to get ? = 450. Next, take 20% of 450: 0.20 × 450 = 90. d. When all of the staplers sold, the amount collected is $2.50 × 12 = $30. Since a dozen staplers cost $10, the profit is $20. Next, set up a proportion: $20 profit ?  initia l $10 =  10 0 Cross multiply to get (100)(20) = (10)(?), or 2,000 = (10)(?). Divide both sides by 10 to get ? = 200. Thus, the rate of profit is 200%. c. Find the net loss: $50 – $38 = $12. Next, set up a proportion: $12 loss ?  initial $50 =  10 0 Cross multiply to get 12 × 100 = 50 × ?, or 1,200 = 50 × ?. Divide both sides by 50 to get ? = 24. Thus, there is a 24% loss. b. $130 – 10% of 130 = 130 – 13 = $117. Next take 15% of 117 = 0.15 × 117 = 17.55. Deduct this amount: 117 – 17.55 = $99.45. Choice a, 97.5 is incorrect because this represents a 25% reduction in price. You cannot add 10% and 15% and deduct 25%. c. The printer will sell for 115% of the cost. 115% × $85 = 1.15 × 85 = 97.75. This question can also be solved in two steps: 15% of 85 = $12.75 markup. Add $12.75 to $85 (the cost) to get $97.75. a. If the price of the car is p, then you know that the price of the car plus 8.5% of that price added up to $14,105; 8.5% equals 0.085. Thus, p + .085p = 14,105; 1.085p = 14,105. Dividing both sides by 1.085 yields p = $13,000. b. You can solve this problem by asking yourself: “2,380 is what percent of 34,000?” and then expressing this question mathematically: ? 2,380 =  10 0 × 34,000. Divide both sides by 2,380 ? 34,000 to get  34,0 00 =  10 0 . Cross multiply to get 238,000 = (34,000)(?). Divide both sides by 34,000 to get 7. Thus, the answer is 7%.

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600 pounds. Thus, you get:

5,000 = 150 × ?. Divide both sides by 150 to get ? = 3313. Thus, there was a 3313% increase. 47. a. Use the proportion: ? Change  =  10 0 Initial where the change = 200 – 150 = 50, and the initial value is 200. Thus, you have: 50 ?  20 0 = 10 0 Cross multiply to get 50 × 100 = 200 × ?, or 5,000 = 200 × ?. Divide both sides by 200 to get ? = 25. Thus, there was a 25% decrease.

60  60 0

Cross multiplying yields 60 × 100 = 600 × ?, or 6,000 = 600 × ?. Divide both sides by 600 to get ? = 10. Thus, there is a 10% error, choice a. 49. b. Draining half the 5-gallon tank leaves 2.5 gallons inside. Because you know the solution is a 50-50 mixture, there must be 1.25 gallons of water present at this point. After adding 2 gallons of water, there will be 1.25 + 2, or 3.25 gallons of water in the final mixture.

48. a. Use the proportion: Difference in values  Actual value

? = 10 0

? = 10 0

Here the difference in values is 600 pounds – 540 pounds = 60 pounds. The actual value is

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C H A P T E R

6

Number Series

S

ome number series can be categorized as arithmetic or geometric. Other number series are neither arithmetic or geometric and thus must be analyzed in search of a pattern. Let’s review the two general types of number series you may see on the civil service exam.



Arithmetic Series

This type of number series progresses by adding (or subtracting) a constant number to each term. For example, look at the series: 4, 7, 10, 13, 16, . . . Notice that each term is 3 more than the term that comes before it. Therefore, this is an arithmetic series with a common difference of 3.

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–NUMBER SERIES–



Geometric Series

Geometric series progress by multiplying (or dividing) each term by a constant number to get the next term. For example, look at the series: 1 , 1, 2, 4, 8, 16, 32, . . . 2

Notice that each term is two times the prior term. Therefore, this is a geometric series with a common ratio of 2.



Letter Series

Instead of containing numbers, letter series use the relationships of the letters in the alphabet to generate patterns. Study the series and try to figure out what the relationship is. For example, look at the series: ABC, CBA, DEF, FED, GHI, Which answer choice will correctly fill in the blank—IJK, JKL, LKJ, or IHG? Notice that the first triplet of the series is ABC. The next triplet contains the same 3 letters listed in reverse order: CBA. The third triplet is DEF, followed by its inverse FED. Next comes GHI, so the missing 3 letters will be GHI in reverse order, or IHG.



Symbol Series

Symbol series are visual series based on the relationship between images. Carefully analyze this visual series to find the pattern. For example, look at the following symbol series:  What symbol comes next— , , , or

? Notice that the position of each arrow can be found by rotating the previous arrow 45° clockwise. Thus, the next arrow will be .

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–NUMBER SERIES–



Practice Questions

5. What number is missing from the following series? 1, 4, 6, 1, , 6, 1 a. 6 b. 4 c. 1 d. 2

1. What number is missing from the following series? 18, 14, , 6, 2 a. 12 b. 10 c. 8 d. 4

6. What number is missing from the following series? 9.7, 10.1, , 10.9, 11.3 a. 9.7 b. 9.9 c. 10.5 d. 11.3

2. What number is missing from the following series? 5, 15, 45, , 405 a. 50 b. 60 c. 75 d. 135

7. What number is missing from the following series? 0, 1, 8, 27, a. 34 b. 54 c. 64 d. 76

3. What number is missing from the following series? 72, 67, , 57, 52 a. 62 b. 63 c. 59 d. 58

8. Look at this series: 567, 542, 517, 492, . . . . What number should come next? a. 499 b. 483 c. 477 d. 467

4. What number is missing from the following series? 8.2, , 7.6, 7.3, 7.0 a. 8.1 b. 8 c. 7.9 d. 7.8

9. What number is missing from the following series? 90, 45, ,11.25, 5.625 a. 0 b. 12.5 c. 16 d. 22.5

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14. What number is missing from the following series? 1 1 2 1 , 1 , 3,240 , 540 5 5,

10. What number is missing from the following series? , 0.34, 0.068, 0.0136 a. 1.7 b. .408 c. 4.08 d. 17

a. b. c. d.

11. Look at this series: 2, 1, 12, 14, . . . . What number should come next? a. b. c. d.

2 3 0 1 4 5 1 9 0 1   270

15. What number is missing from the following series? 30, , 27, 25, 12, 24 a. 2912 b. 29 c. 2812 d. 28

1  3 1  8 2  8 1 1 6

12. What number is missing from the following series? 0, 1, , 6, 10, 15 a. 2 b. 3 c. 4 d. 5

16. What number is missing from the following series? 10, 12, 16, 22, 30, 40, a. 33 b. 34 c. 40 d. 52

13. What number is missing from the following series? 4, 1, 5, 4, 1, 7, 4, 1, 9, 4, 1, a. 1 b. 4 c. 9 d. 11

17. What number is missing from the following series? –12, 6, 4, –13, 7, 3, –14, ,2 a. 8 b. 10 c. 12 d. 13 18. What number is missing from the following series? 5,423; 5,548; 5,673; 5,798; a. 5,823 b. 5,848 c. 5,923 d. 5,948 80

–NUMBER SERIES–

19. What number is missing from the following series? 6, 11, 16, 16, 21, 26, 26, a. 16 b. 26 c. 30 d. 31

24. Look at this series: 0.2, 15, 0.4, 25, 0.8, 45, . . . . What number should come next? a. 180 b. 0.7 c. 1.6 d. 0.16

20. What number is missing from the following series? 10, 14, 84, 88, 264, a. 18 b. 188 c. 268 d. 334

25. Look at this series: 1.5, 2.3, 3.1, 3.9, . . . . What number should come next? a. 4.2 b. 4.4 c. 4.7 d. 5.1

21. What number is missing from the following series? 38, 20, 5, –7, –16, a. –25 b. –22 c. –20 d. –19

26. Look at this series: 29, 27, 28, 26, 27, 25, . . . . What number should come next? a. 23 b. 24 c. 26 d. 27

22. What number is missing from the following series? 9, 8, 16, 15, , 29, 58 a. 30 b. 14 c. 9 d. 8

27. Look at this series: 31, 29, 24, 22, 17, . . . . What number should come next? a. 15 b. 14 c. 13 d. 12

23. Look at this series: 53, 53, , 40, 27, 27, . . . . What number should fill the blank? a. 14 b. 38 c. 40 d. 51

28. Look at this series: 10, 34, 12, 31, , 28, 16, . . . . What number should fill the blank? a. 14 b. 18 c. 30 d. 34

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–NUMBER SERIES–

29. What is the missing term in the following number pattern? 240, 120, 60, 30, 15, , 334

33. Look at this series: 8, 22, 12, 16, 22, 20, 24, . . . . What two numbers should come next? a. 28, 32 b. 28, 22 c. 22, 28 d. 22, 26

a. 712 b. 914 c. 10 d. 1114

34. If the pattern 12, 14, 18, 116 , . . . is continued, what is the denominator of the tenth term? a. 64 b. 212 c. 512 d. 1,024

30. Look at this series: 3, 4, 7, 8, 11, 12, . . . . What number should come next? a. 7 b. 10 c. 14 d. 15

35. Look at this series: 14, 28, 20, 40, 32, 64, . . . . What number should come next? a. 52 b. 56 c. 96 d. 128

31. Look at this series: 1, 4, 9, 5, 17, . . . . What number should come next? a. 6 b. 8 c. 22 d. 25

36. Look at this series: 9, 12, 11, 14, 13, 16, 15, . . . . What two numbers should come next? a. 14, 13 b. 8, 21 c. 14, 17 d. 18, 17

32. Look at this series: 1, 78, 34, 58, . . . . What number should come next? a. b. c. d.

2  3 1  2 3  8 1  4

37. Look at this series: 21, 24, 30, 21, 36, 42, . . . . What number should come next? a. 21 b. 27 c. 42 d. 46

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38. Look at this series: XX, XVI, XII, VIII, . . . . What number should come next? a. IV b. V c. VI d. III

43. Select the letters that best complete the following sequence. ELFA, GLHA, ILJA, , MLNA a. OLPA b. KLMA c. LLMA d. KLLA

39. Look at this series: J14, L11, N8, P5, . . . . What number should come next? a. Q2 b. Q3 c. R2 d. S2

44. Select the pattern that best completes the following sequence.

a. b. c.

40. Look at this series: VI, 10, V, 11, IV, 12, . . . . What number should come next? a. VII b. III c. IX d. 13

d. 45. Select the pattern that best completes the following sequence.

a. b.

41. Select the answer choice that best completes the following sequence. JAK, KBL, LCM, MDN, a. OEP b. NEO c. MEN d. PFQ

c. d. 46. Select the pattern that best completes the following sequence.

42. Select the letters that best complete the following sequence. QPO, NML, KJI, , EDC a. HGF b. CAB c. JKL d. GHI

a. b. c. d.

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47. What best completes the following sequence?

49. What best completes the following sequence?

a.

a.

b.

b.

c.

c.

d.

d. 50. What best completes the following sequence?

48. What best completes the following sequence?

a.

a.

b.

b.

c.

c.

d.

d.

84

–NUMBER SERIES–



Answers

1. b. This is an arithmetic series that decreases by four as the series progresses. Thus, the missing number is 14 – 4 = 10. You can check that this is correct by applying the rule to the 10: 10 – 4 = 6, which is in fact the next term. 2. d. This is a geometric series. You multiply each term by 3 to get the next term. The missing term is 45 × 3 = 135. You can check that this rule works by multiplying 135 by 3. This yields 405, which is the next term. 3. a. This is an arithmetic series. Each term is 5 less than the prior term. To find the missing term, subtract 5 from 67 to get 62. Next, check that the rule is correct by verifying 62 – 5 = 57, the next term. 4. c. This is an arithmetic series with a common difference of 0.3. This simply means that each term is 0.3 less than the term before it. 8.2 – 0.3 = 7.9, so the missing term is 7.9. To check that you found the right rule, subtract 0.3 from 7.9 to get 7.6, the next term. 5. b. This series is neither arithmetic or geometric. It is simply three numbers repeating over and over in order. The numbers 1, 4, and 6 repeat. Thus, the missing number is 4. 6. c. This is an arithmetic series. Each term is 0.4 greater than the previous term. 10.1 + 0.4 = 10.5. Using this rule, the term following 10.5 should be 10.5 + 0.4 = 10.9, and it is. Thus, you know you used the correct rule. 7. c. This series is neither arithmetic or geometric. If you look carefully at the numbers, you should notice that each is a cube of a number. In other words, 0, 1, 8, 27 corresponds to 03, 13, 23, 33, so the next term should equal 43, or 64.

8. d. This is an arithmetic series; each number is 25 less than the previous number. Thus, the answer is 492 – 25 = 467. 9. d. This is a geometric series with a common ratio of 12. In other words, each term is 12 of the term that precedes it. Thus, the missing term is 12 of 45; 12 × 45 = 22.5. To check that you used the correct rule, take 12 of 22.5: 22.5 × 12 = 11.25. This is the next term in the series so you know you are right. 10. a. This is a geometric series with a common ratio of 0.2. In other words, each term is 0.2 times the term that precedes it. You can divide 0.34 by 0.2 to figure out what the first term is. 0.34 ÷ 0.2 = 1.7. You can check that you have the correct answer by applying the rule: 0.34 × 0.2 = 0.068. 11. b. This is a geometric series; each number is one-half of the previous number. Thus, the next number should be 12 × 14 = 18. 12. b. Here the numbers are increasing, but the amount by which they are increasing is increasing as well. 0 (+ 1) 1 (+2) 3 (+3) 6 (+4) 10 (+5) 15. Thus, the missing number is 3. 13. d. Consider this series as a triplet. The first 2 terms of the triplet are always 4 followed by 1. Notice that every third term gets 2 added to it: 4, 1, 5, 4, 1, 7, 4, 1, 9, 4, 1, . Thus, the missing number is 9 + 2 = 11. 14. c. This is a geometric series with a common ratio of 61. This means that each term is the prior term multiplied by 61. This is more evident when looking at the last two terms of the 1 1  (× ) series: 52 (× 61) 115 (× 61) (× 61)  540 6 1 1 1 1  3,2 40 . Thus, the missing term is 1 5 × 6 = 9 0. 15. c. This is an arithmetic series with a common difference of 112. The missing term is 30 – 112 = 2812. You can check your work by applying

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–NUMBER SERIES–

16.

17.

18.

19.

20.

21.

the rule to 2812; 2812 – 112 = 27, which is the next term. d. Here the numbers are increasing. Notice that it is not a steady common difference (arithmetic), nor a steady common ratio (geometric). The amount of increase corresponds more to an addition, and each term is increasing by having a larger number added to it. The pattern here is 10 (+2) 12 (+4) 16 (+6) 22 (+8) 30 (+10) 40 (+12) . Thus, the missing number is 40 + 12, or 52. a. Here the series can be considered as triplets. The first number of each triplet is decreased by 1: –12, 6, 4 –13, 7, 3 –14, , 2. The second number of each triplet is increased by 1: –12, 6, 4 –13, 7, 3 –14, , 2. Thus, the missing number is 7 + 1 = 8. (Notice also that the third number in each triplet is decreased by 1: –12, 6, 4 –13, 7, 3 –14, , 2.) c. This is an arithmetic series in which each number is increased by 125. The missing number will be 5,798 + 125, or 5,923. d. The pattern here is +5, +5, repeat, +5, +5, repeat. 6 (+5) 11 (+5) 16 (repeat ) 16 (+5) 21 (+5) 26 (repeat ) 26 (+5) Thus, the missing number is 26 + 5 = 31. c. The pattern here is +4, × 6, +4, × 6, and so forth. 10 (+ 4) 14 (× 6) 84 (+ 4) 88 (× 6) 264 (+ 4) Thus, the missing number is 264 + 4 = 268. b. Here the numbers are decreasing, though not by a steady amount or by a common ratio. The pattern of decrease is: 38 (minus 3 × 6) 20 (minus 3 × 5) 5 (minus 3 × 4) –7 (minus 3 × 3) –16 (minus 3 × 2) Thus, the missing number is –16 minus 3 × 2, or –16 – 6 = –22.

22. a. Here the pattern is – 1, × 2, – 1, × 2, and so forth: 9 (– 1) 8 (× 2) 16 (–1) 15 (× 2) (– 1) 29 (× 2) 58 Thus, the missing number is 15 × 2 = 30. You can check that you are right by subtracting 1; 30 – 1 = 29, which is the next number in the series. 23. c. In this series, each number is repeated, then 13 is subtracted to arrive at the next number. Thus, the missing number is 53 – 13 = 40. 24. c. This is a multiplication series with repetition. The decimals (0.2, 0.4, 0.8) are repeated by a fraction with the same value (15, 25, 45) and are then multiplied by 2. Thus, the next number will be 0.8 × 2, or 1.6. 25. c. In this arithmetic series, each number increases by 0.8. Thus, the next number should be 3.9 + 0.8 = 4.7, choice c. 26. c. In this simple alternating addition and subtraction series, 2 is subtracted, then 1 is added, and so on. Thus, the next number should be 25 + 1, or 26. 27. a. This is an alternating subtraction series, which subtracts 2, then 5. Thus, the next number will be 17 – 2 = 15. 28. a. This is an alternating addition and subtraction series. The first series begins with 10 and adds 2 (10, 12, 14, 16); the second begins with 34 and subtracts 3 (34, 31, 28). Thus, the number that belongs in the blank is 14. 29. a. Each number in the pattern is one-half of the previous number. Half of 15 is 712. You can check the pattern by taking half of 712, which is 334, the next term. 30. d. This alternating addition series begins with 3. 1 is added to give 4; then 3 is added to give 7; then 1 is added, and so on. Thus, the next number will be 12 + 3 = 15.

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31. a. This is an alternating series. In the first pattern, 8 is added (1, 9, 17); in the second pattern, 1 is added (4, 5, 6). Thus, the next number will be 6. 32. b. This is a subtraction series. Each number decreases by 18. The next number is 58 – 18, which is 48, or 12. 33. c. This is an alternating repetition series, with a random number, 22, introduced as every third number into an otherwise simple addition series. In the addition series, 4 is added to each number to arrive at the next number. Thus, the next two numbers will be 22 (the random number) followed 24 + 4, or 28. 34. d. Given the pattern 12, 14, 18, 116 . . . notice that the denominators double as the pattern advances. There are 4 terms so far. The fifth term will have a denominator of 32, the sixth term will be 64, the seventh term will be 128, the eighth term will be 256, the ninth term will be 512, and the tenth term will be 1,024. 1 So the tenth term is  1,0 24 . 35. b. This is an alternating multiplication and subtraction series: First, multiply by 2, and then subtract 8. The next term will be 64 – 8 = 56. 36. d. This is an alternating addition and subtraction series. First, 3 is added, then 1 is subtracted; then 3 is added, 1 subtracted, and so on. Thus the next term will be 15 + 3 = 18. The term after that will be 18 – 1 = 17. 37. a. This is an addition series with a random number, 21, introduced as every third number. In the series, 6 is added to each number except 21, to arrive at the next number. The next number is the random number, 21. 38. a. This is a subtraction series; each number (represented in Roman numerals) is 4 less than the previous number. XX = 20, XVI = 16, XII = 12, VIII = 8, so the next number

39.

40.

41.

42.

43.

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should be 4. In Roman numerals, 4 is written as IV, choice a. c. In this series, the letters progress by 2 (J, L, N, P), while the numbers decrease by 3 (14, 11, 8, 5). Thus, the next term will be R2, choice c. b. This is an alternating addition and subtraction series. Roman numerals alternate with standard numbers. In the Roman numeral pattern, each number decreases by 1 (VI, V, IV, III, corresponding to 6, 5, 4, 3). In the standard numeral pattern, each number increases by 1 (10, 11, 12, 13). Thus, the next number should be the Roman numeral for 3, which is III. b. If you consider each triplet of letters, the first letter in each triplet progresses from J  K L M . The second letter in each triplet progresses from A B C D , and the third letter in each triplet progresses from K L M N . Therefore, the last triplet should be NEO. a. If you look carefully at this sequence, you will notice that the entire sequence is the alphabet (starting at C) written backward. Therefore, the missing three letters are HGF. d. If you look at the first letter in each quadruplet, you can see that one letter is skipped: ELFA, GLHA, ILJA, , MLNA, so the first missing letter is K. Looking at the second letter in each quadruplet, you see that the letter L is constant: ELFA, GLHA, ILJA, , MLNA, so the second missing letter must be L. Next, look at the third letter in each quadruplet: ELFA, GLHA, ILJA, , MLNA. Again, one letter is skipped, so the missing letter is L. Finally, look at the last letter in each quadruplet: ELFA, GLHA, ILJA, , MLNA. The letter A is a constant, so the last missing letter is A. Thus, the entire missing piece is KLLA.

–NUMBER SERIES–

44. b. Notice that each group of symbols has three versions of the same shape, the middle version being the largest: . Also, a black and a white version of the shape border this large middle shape. Notice that the circle is on the right and the black triangle is on the left. The missing shapes will be squares (thus choice c is incorrect). The next two shapes will be a large square with the black square on the right: . 45. a. The first group contains a square between two triangles. Next, there is a circle between 2 squares. Third, there is a diamond between two circles. The last set has a rectangle in the middle. It should be between two diamonds. 46. b. This is an alternating pattern. First, the two arrows point right, then one points up and one points down. Thus, the next part of the sequence should contain the two arrows pointing right. 47. d. The first image is reflected (flipped), generating the second image. Then the second is

flipped to form the third. Thus, the fourth image will be the reflection of which will look like this: . 48. a. Look at the number of dots on each domino in each triplet: . The first triplet has 5 dots, 3 dots, 1 dot. The next triplet has 1 dot, 3 dots, 5 dots. The last triplet ends with 1 dot. It is safe to assume that the pattern here is 5-3-1; 1-3-5; and 5-3-1. The missing 2 dominos are , the 5 and the 3. 49. c. Notice that the first and the third segments are upside-down versions of each other. The second and the fourth should also be upside-down versions of each other. Thus, the missing piece of the last segment looks like this: . 50. c. The first and the third figures swap the inner shape for the outer shape. The second and fourth would then be expected to swap the top and bottom shapes. Thus, you would expect the missing shape to be a square on top of a circle, choice c.

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C H A P T E R

7

Word Problems

I

n addition to dealing with basic operations, fractions, decimals, and percents, the civil service exam may use word problems to test your math and logic skils. This chapter will introduce a few common types of word problems.



Ratios and Proportions

A ratio is a way of comparing two or more numbers. There are several different ways to write ratios. Here are some examples. ■ ■ ■ ■

with the word to: 1 to 2 using a colon (:) to separate the numbers: 1 : 2 using the term for every: 1 for every 2 separated by a division sign or fraction bar: 12

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–WORD PROBLEMS–

Usually, a fraction represents a part over a whole: part  wh ole

Often, a ratio represents a part over a part: part  part

But ratios can also represent a part over a whole: part  wh ole

When a ratio represents a part over a part, you can often find the whole if you know all the parts. A proportion is a way of relating two ratios to one another. If you equate a given ratio to the part that you know, you can find an unknown part. Once you know the unknown parts, you can calculate the whole. Many word problems require you to use ratios and proportions to find unknown values. Example: If the ratio of union workers to nonunion workers is 2:3 and there are 360 nonunion workers, how many workers are there in all? Here, you are given a 2:3 ratio. You know one part: that there are 360 nonunion workers. You can set up a proportion in order to calculate the unknown part: 2  3

? = 36 0

Cross multiply to get 360 × 2 = 3 × ?, or 720 = 3 × ?. Now, divide both sides by 3 to get ? = 240. This is the missing part: the number of union workers. Finally, add the number of union workers to nonunion workers to get the whole: 360 + 240 = 600.



Work and Salaries in Word Problems

Some word problems deal with salaries. You should be familiar with the following salary schedules: ■ ■ ■ ■ ■ ■ ■

per hour: amount earned each hour daily: amount earned each day weekly: amount earned each week semiweekly: amount earned twice a week semimonthly: amount earned twice a month monthly: amount earned each month annually: amount earned each year Other problems involving work need to be dissected logically. For example, consider the following.

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–WORD PROBLEMS–

Example: If 14 workers can complete a job in 2 days, how long will it take 4 workers to complete the same job? Assume all workers work at the same rate. Most people try to set up the following proportion when confronted with this scenario: 14 wo r kers 4 workers  =  2 d ays ? days

Notice that the ? in the denominator of the second ratio will be smaller than the 2 days in the denominator of the first ratio. Does it make sense that 4 workers will be able to finish the job of 14 workers in less than 2 days? No. This sort of question needs to be broken apart logically. If 14 workers can complete the job in 2 days, it will take one person 14 times as long to complete the same job: 28 days. It will take 4 people 14 as long to complete this amount of work, or 7 days.



Tank and Pipe Word Problems

Tank and pipe word problems must also be solved logically. Tank and pipe questions involve the filling and draining of tanks through various pipes. Once you see what the net (overall) effect is, you are able to solve the question posed to you. Example: A tank is partly filled with water. Pipe X leads into the tank and can fill the entire tank in 4 minutes. Pipe Y drains the tank and can drain the entire tank in 3 minutes. At a certain point in time, the tank is halfway full, and the valves leading to pipes X and Y are closed. When these valves are opened simultaneously, how long will it take for the tank to drain? First, consider Pipe X. It can fill the tank in 4 minutes. This means that for every minute that goes by, 14 of the tank would get filled. Next, consider Pipe Y. This pipe can empty the tank in 3 minutes. This means that for every minute that goes by, 13 of the tank would get drained. When you consider these fractions as twelfths, you see that Pipe X fills 132 per minute and Pipe Y drains 142 per minute. The net effect is a draining of 112 of the tank every minute. Since the tank starts out 12 full (or 162 full), it will take 6 minutes to drain the 162 of water (at the rate of 112 out per minute).



Distance Word Problems

Distance questions can be solved with the formula D = RT, where D = distance, R = rate, and T = time, assuming that a constant rate is maintained. Here you have the flexibility to use many different combinations of rates, distances, and times, so long as the units you use in the equation match each other. For example, rates can be measured in meters per second, kilometers per hour, feet per second, miles per hour, and so forth. Just be sure that if you use, for example, a rate in miles per hour as your R in the equation, that your D is in miles, and your T is in hours.

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–WORD PROBLEMS–

Example: Train A leaves its station and travels at a constant rate of 65 miles per hour in an eastward direction. At the same time, Train B leaves a western station heading east at a constant rate of 70 miles per hour. If the 2 trains pass each other after 3 hours, how far apart were they initially? The 2 trains’ initial distance apart equals the sum of the distance each travels in 3 hours. Using D = RT, you know Train A travels a distance of (65)(3) = 195 miles, and Train B travels (70)(3) = 210 miles. This means that they were 195 + 210 = 405 miles apart initially. It is helpful to draw a diagram to understand this better: Train A

Train B

DA = RT

DA = RT

initial distance apart



Practice Questions

3. Greg had $12,000 in his savings account. Of this amount, he transferred 13 into checking, 14 into a certificate of deposit, and spent 18 on a computer system. How much money remains in his savings account? a. $3,500 b. $5,000 c. $5,600 d. $6,000

1. Pete made $4,000 in January, $3,500 in February, and $4,500 in March. If he put 30% of his total earnings into his checking account and the rest into his saving account, how much money does he have in his checking account? a. $3,600 b. $4,200 c. $6,300 d. $8,400

4. If two pieces of wood measuring 212 feet and 313 feet are laid end to end, how long will their combined length be? a. 5 feet 5 inches b. 5 feet 10 inches c. 6 feet d. 6 feet 5 inches

2. Denise had $120. She gave 18 of this amount to Suzanne. She then gave 14 of the remainder to Darlene. How much money does Denise have left? a. $26.25 b. $30.00 c. $78.75 d. $80.00

5. A shipment of cable weighs 3.2 lbs. per foot. If the total weight of 3 identical reels of cable is 6,720 lbs, how many feet of cable are in each reel? a. 64,512 feet b. 21,504 feet c. 2,000 feet d. 700 feet

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–WORD PROBLEMS–

6. A school is purchasing 5 monitors at $175 each, 3 printers at $120 each, and 8 surge suppressors at $18 each. If the school receives a 12% discount, what is the final cost (excluding tax)? a. $1,379.00 b. $1,313.52 c. $1,213.52 d. $1,200.00

10. Mia can hike 1.3 miles in 45 minutes. Which equation could be used to find d, the distance in miles that Mia can hike in 3 hours?

7. The Huntington Golf Club has a ratio of two women to every three men. A 2:3 ratio is equivalent to which of the following ratios? a. 3:2 b. 4:8 c. 8:12 d. 4:12

11. If Jack always spends $18 on gaming equipment in a week, how much does he spend in 6 weeks? a. $60 b. $48 c. $108 d. $180

a. b. c. d.

d 0.75  =  3 1.3 1.3 d  0.7 5 = 3 3 0.75  =   1.3 d d 0.75  =   1.3 3

12. If it takes a machine 5 minutes to build 3 components, how long would it take the same machine to build 18 components? a. 90 minutes b. 18 minutes c. 15 minutes d. 30 minutes

8. A map drawn to scale shows that the distance between 2 towns is 3 inches. If the scale is such that 1 inch equals 1 kilometer, how far away are the two towns in kilometers? a. 3 miles b. 3 kilometers c. 30 miles d. 30 kilometers

13. Dr. Martin sees an average of 2.5 patients per hour. If she takes an hour lunch break, about how many patients does she see during the typical 9-to-5 work day? a. 16 b. 18 c. 20 d. 22

9. If it takes 27 nails to build 3 boxes, how many nails will it take to build 7 boxes? a. 64 b. 72 c. 56 d. 63

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–WORD PROBLEMS–

18. A construction job calls for 256 tons of sand. Four trucks, each filled with 34 tons of sand, arrive on the job. Is there enough sand, or is there too much sand for the job? a. There is not enough sand; 16 ton more is needed. b. There is not enough sand; 13 ton more is needed. c. There is 13 ton more sand than is needed. d. There is 16 ton more sand than is needed.

14. A diagram drawn to scale shows a diagonal of 12 centimeters. If the scale is 1.5 centimeters = 1 foot, how long is the actual diagonal? a. 8 feet b. 7.5 feet c. 6.8 feet d. 6 feet 15. The height of the Statue of Liberty from foundation to torch is 305 feet 1 inch. Webster’s American Mini-Golf has a 1:60 scale model of the statue. Approximately how tall is the scale model? a. 5 inches b. 5 feet 1 inch c. 6 feet 5 inches d. 18,305 feet

19. Jessica earns a semimonthly salary of $1,200. What is her yearly salary? a. $144,000 b. $48,000 c. $28,800 d. $14,400

16. Scott can pot 100 plants in 30 minutes. Henri can do the same job in 60 minutes. If they worked together, how many minutes would it take them to pot 200 plants? a. 20 b. 30 c. 40 d. 60

20. During a normal 40-hour workweek, Mitch earns $800. His boss wants him to work this weekend, and Mitch will get paid time and a half for these overtime hours. How much will Mitch make for 10 weekend hours? a. $200 b. $240 c. $300 d. $340

17. Francine and Lydia are in the same book club, and both are reading the same 350-page novel. Francine has read 45 of the novel. Lydia has read half as much as Francine. What is the ratio of the number of pages Lydia has read to the number of pages in the novel? a. 1:2 b. 2:5 c. 2:3 d. 1:4

21. Gary earns $22 an hour as a lab technician. Monday he worked 5 hours, Tuesday he worked 8 hours, and Wednesday he worked 412 hours. How much did he earn during those three days? a. $363.00 b. $374.00 c. $385.00 d. $407.00

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–WORD PROBLEMS–

22. This month Louise earned $2,300 as her gross pay. Of this amount, $160.45 was deducted for FICA tax, $82.50 was deducted for state tax, $73.25 was deducted for city tax, and $100 was diverted to her 401(k). How much was her net paycheck? a. $1,883.80 b. $1,888.30 c. $1,983.80 d. $1,988.33

26. John earns $1,600 a month plus 8% commission on all sales. He sold $825 worth of merchandise during November, $980 worth of merchandise during December, and $600 worth of merchandise during January. What were his total earnings for these three months? a. $1,792.40 b. $2,597.40 c. $1,924.00 d. $4,992.40

23. Two men can load a truck in 4 hours. How many trucks can they load in 6 hours? a. 1 b. 112 c. 2 d. 212

27. Four machines can complete a job in 6 hours. How long will it take 3 machines to complete the same job? a. 4 hours b. 8 hours c. 10 hours d. 12 hours

24. A machine can assemble 400 parts in half an hour. Of the 400 parts, 5% will be defective. If two machines are working, how many nondefective parts will be assembled in 5 hours? a. 800 b. 1,600 c. 3,800 d. 7,600

28. One construction job can be completed by 16 workers in 10 days. How many days would it take 8 workers to complete the job? a. 12 days b. 16 days c. 18 days d. 20 days 29. A job can be completed by 6 workers in 18 days. How many days would it take 9 workers to complete the job? a. 12 days b. 16 days c. 18 days d. 20 days

25. Kate’s daily salary is $120. If she worked 24 days this month, how much did she earn? a. $3,600 b. $3,200 c. $3,000 d. $2,880

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–WORD PROBLEMS–

33. Alison and Artie worked on a project together. Alison put in 18 hours of work and Artie put in 24 hours of work. The contract for the entire project was $7,000. If the two decide to split the money up according to the ratio of the amount of time each put into the project, how much will Artie get? a. $3,000 b. $3,500 c. $4,000 d. $4,500

30. Nine workers working at the same pace can complete a job in 12 days. If this job must be completed in 3 days, how many workers should be assigned? a. 27 b. 30 c. 36 d. 48 31. When Anthony and Elise work together they can complete a task in 3 hours. When Anthony works alone he can complete the same task in 8 hours. How long would it take Elise to complete the task alone? a. 612 hours b. 6 hours c. 445 hours d. 4 hours

34. Tina’s semiweekly salary is $400. Jim’s semimonthly salary is $1,800. If both of them work a standard 40-hour workweek, who earns more for the month of February? (Assume that this is NOT a leap year.) a. Tina by $1,400 b. Jim by $400 c. Tina by $400 d. Jim by $1,400

32. Rose and Marie worked on a project together. Rose put in 40 hours of work and Marie put in 60 hours of work. The contract for the entire project paid $2,000. The women decide to split the money up according to the ratio of the amount of time each put into the project. How much did Marie get? a. $400 b. $600 c. $1,000 d. $1,200

35. Kayla can type 60 reports in 3 hours. Ethan can type 110 reports in 6 hours. Working together, how long will it take them to type 375 reports? a. 13 hours b. 12 hours c. 10 hours d. 9 hours 36. For an employee who works a 30-hour workweek, a $28,000 yearly salary translates into which of the following hourly wages? a. $13.46 b. $14.50 c. $17.95 d. $19.46

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–WORD PROBLEMS–

40. Rudy forgot to replace his gas cap the last time he filled up his car with gas. The gas is evaporating out of his 14-gallon tank at a constant rate of 1  gallon per day. How much gas does Rudy lose 3 in 1 week?

37. A tank containing fluid is half full. A pipe that can fill 116 of the tank per minute begins letting more fluid in. At the same time, a drain that can empty 18 of the tank in one minute is opened. How long will it take to empty the tank? a. 8 minutes b. 16 minutes c. 18 minutes d. 32 minutes

a. 2 gallons b. 213 gallons c. 313 gallons d. 423 gallons

38. Pipe T leads into a tank and Pipe V drains the tank. Pipe T can fill the entire tank in 6 minutes. Pipe V can drain the entire tank in 4 minutes. At a certain point in time, the valves leading to both pipes are shut and the tank is 14 full. If both valves are opened simultaneously, how long will it take for the pipe to drain? a. 2 minutes b. 3 minutes c. 4 minutes d. 6 minutes

41. Pipe A leads into a tank and Pipe B drains the tank. Pipe A can fill the entire tank in 10 minutes. Pipe B can drain the entire tank in 8 minutes. At a certain point in time, the valves leading to both pipes are shut and the tank is 12 full. If both valves are opened simultaneously, how long will it take for the pipe to drain? a. 18 minutes b. 20 minutes c. 22 minutes d. 24 minutes

39. For every 10,000 liters of water that pass through a filtering system, 0.7 gram of a pollutant is removed. How many grams of the pollutant are removed when 106 liters have been filtered? a. 7 b. 70 c. 700 d. 7,000

42. A car travels at a constant rate of 60 kilometers per hour for 3 hours. How far did the car travel? a. 180 kilometers b. 180 miles c. 18 kilometers d. 18 miles 43. If Michelle runs at a constant rate of 2.5 meters per second, how long will it take her to run 1 kilometer? a. 4 minutes b. 40 minutes c. 400 seconds d. 4000 seconds

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–WORD PROBLEMS–

48. A train leaves a station traveling west at 60 miles per hour. At the same time, another train heads east on a parallel track, traveling at a rate of 70 miles per hour. If the 2 trains are initially 700 miles apart, how far apart are they after 1 hour? a. 630 miles b. 610 miles c. 570 miles d. 560 miles

44. It took T.J. 20 minutes to jog 2 miles. What was his average speed in miles per hour? a. 40 miles per hour b. 10 miles per hour c. 8 miles per hour d. 6 miles per hour 45. Sipora drove to Stephanie’s house at a constant rate of 45 mph. If Stephanie’s house is 220 miles away and Sipora wants to get home in exactly 4 hours, how fast should she drive? a. 50 miles per hour b. 55 miles per hour c. 60 miles per hour d. 65 miles per hour

49. Train A leaves Station A at 6 P.M., traveling east at a constant rate of 70 miles per hour. At the same time, Train B leaves Station B, traveling west at a constant rate of 90 miles per hour. If the two trains pass each other at 8 P.M., then how far apart are the two stations? a. 280 miles b. 300 miles c. 320 miles d. 360 miles

46. Amy can run 8 miles at a constant rate in 40 minutes. Sharon can run 12 miles at a constant rate in an hour. Who has a faster rate? a. Amy b. Sharon c. They both run at the same rate. d. It cannot be determined by the information given.

50. An eastbound train destined for Stony Brook Station leaves Penn Station at 4 P.M., traveling at a rate of 60 miles per hour. At the same time, a westbound train departs the Stony Brook Station on its way to Penn Station. If the westbound train travels at a constant speed of 70 miles per hour and the two stations are 260 miles apart, then at what time will the two trains pass each other? a. 4:30 P.M. b. 5:00 P.M. c. 5:30 P.M. d. 6:00 P.M.

47. Train A travels at 60 mph for 20 minutes. Train B travels at 55 miles per hour for 30 minutes. If both trains are traveling at a constant rate, which train would have traveled a greater distance after the time periods specified? a. Train A b. Train B c. Both trains traveled the same distance. d. It cannot be determined by the information given.

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–WORD PROBLEMS–



Answers 10. b. To find the distance Mia can hike in 3 hours, first set up the ratio of the distance she can walk in a certain amount of time. 45 minutes is 1.3 miles  equal to 43 of an hour or 0.75 hours  0.75 ho urs . d Then set up the second ratio,  3 ho urs . Set these 2 1.3 d ratios equal to each other:  0.7 5 = 3. 18 11. c. First set up a proportion: 1 = 6x. Cross multiplying yields 18 × 6 = 1 × x, and x = 108. 12. d. First set up a proportion: 53 = 1x8 . Then, cross multiply: 3x = 18 × 5. Then solve for your answer: 3x = 90, so x = 30 minutes. 13. b. 9 to 5 represents an 8-hour work day, less the one hour lunch break yields 7 working hours. Multiply the 7 hours by 2.5 patients per hour = 17.5 patients. Of the choices, 18 patients is the best answer. 1.5 centimeters 12 centimeters = . 14. a. Set up a proportion:  1 foot ? feet Cross multiply to get 1.5 × ? = 12 × 1 , or 1.5 × ? = 12. Divide both sides by 1.5 to get ? = 8 feet. 15. b. First convert the height of the statue to inches: 305 feet × 12 inches = 3,660 inches. The statue is 3,660 + 1, or 3661, inches tall. x Next, set up a proportion: 610 =  3,6 61 . Cross multiply: 60x = 3,661. Divide both sides by 3,661  60: x =  60 ; x is about 61 inches. Convert to feet by dividing by 12: 61 ÷ 12 = 5 r1. Thus, the answer is 5 feet 1 inch, choice b. 16. c. Because this is a rate of work problem, consider what fraction of the job would get done in one minute. Scott would get 310 of the job done while Henri would get 610 of the job done in one minute. Together, they would get: 1 1 2 1 3 1 3 0 + 6 0 = 6 0 + 6 0 = 6 0 = 2 0 of the job done in one minute. Therefore, 20 minutes would be needed to pot 100 plants, and 40 minutes to pot all 200 plants.

1. a. First, calculate the total amount of money: $4,000 + $3,500 + $4,500 = $12,000. He puts 30% of the $12,000, or .30 × $12,000 = $3,600, into the checking account. 2. c. 18 of the $120 went to Suzanne: 18 × 120 = $15. This means there was 120 – 15 = $105 left; 14 of the $105 went to Darlene: 14 × 105 = $26.25. Thus, the amount remaining is 105 – 26.25 = $78.75. 3. a. 13 of 12,000 = 13 × 12,000 = $4,000 went to checking. 14 of 12,000 = 14 × 12,000 = $3,000 went to the CD. And 18 of $12,000 = 18 × 12,000 = $1,500 went to buy the computer. Thus, the amount left equals 12,000 – 4,000 – 3,000 – 1,500 = $3,500. 4. b. 221 feet = 2 feet 6 inches. 331 feet = 3 feet 4 inches. The sum of these values is 5 feet 10 inches. 5. d. Divide the total weight by 3 to figure out how much each of the three reels weighs: 6,720 ÷ 3 = 2,240 pounds each. Next, divide the 3.2 lbs  weight of the reel by  foot : 2,240 pounds ÷ 3.2 pounds  = 700 feet. foot 6. c. Five monitors will cost $175 × 5 = $875; three printers will cost $120 × 3 = $360; eight surge suppressors will cost $18 × 8 = $144. Before the discount, this adds to: $875 + $360 + $144 = $1,379; 12% of $1,379 = .12 × 1,379 = $165.48. Thus, the final cost will be $1,379 – 165.48 = $1,213.52. 7. c. A 2:3 ratio is equivalent to an 8:12 ratio. Multiply the 23 ratio by 44 to get 182. 8. b. If 1 inch on the map denotes 1 kilometer, then 3 inches on the map would represent 3 kilometers. 9. d. First set up a proportion: 237 = 7x. You can reduce the first fraction: 91 = 7x and then cross multiply: 1(x) = 9(7), so x = 63.

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–WORD PROBLEMS–

17. b. Francine has read 45 of 350 pages, or 0.8 × 350 = 280. Lydia has read half of that, or 140. 140  Lydia has read 140 pages out of 350, or  350 . 2 Reduce to 5. 18. d. This is a two-step problem involving multiplication and subtraction. First, determine the amount of sand contained in the 4 trucks. 3 4 12 12  ×  = . Next, reduce:  = 3. Finally, sub4 1 4 4 tract: 3 – 256 = 16. There is 16 ton more than is needed. 19. c. Semimonthly means twice a month. This means she makes 2 × $1,200 = $2,400 per month. Multiply by 12 months per year: $2,400 months    12  year × month = $28,800 a year. 20. c. If he typically earns $800 a week, he makes $800 ÷ 40 hours = $20 per hour. This means he will make 1.5 × 20 = $30 for each overtime $30 hour. 10 hours ×  ho ur = $300. 21. c. First, add up all the hours he worked: 8 + 5 + 412 = 1712 hours. Next, multiply the number of hours he worked by his hourly wage: 17.5 $22 hours ×  ho ur = $385. 22. a. Subtract all of the listed deductions and the diversion to yield the net paycheck: $2,300 – $160.45 – $82.50 – $73.25 – $100 = $1,883.80. 23. b. They can load 1 truck in the first 4 hours and 1  a truck in the next 2 hours, so they can load 2 112 trucks in 6 hours. 24. d. First, if one machine assembles 400 parts in a half hour, it will assemble 800 parts in an hour. Two machines working together will assemble 2 × 800 = 1,600 parts per hour. In 5 hours, they will make 5 × 1,600 = 8,000 parts. Of these 8,000 parts, 5%, will be defective, so 95% will be nondefective. 95% of 8,000 = 95% × 8,000 = 0.95 × 8,000 = 7,600. 25. d. A daily salary is per day. She makes $120 per day times 24 days: $120 × 24 = $2,880.

100

26. d. First, add up all of his merchandise sales: $825 + $980 + $600 = $2,405. Next, take 8% of the $2,405: 0.08 × $2,405 = $192.40. Add the $192.40 commission to his 3 months of pay: $192.40 + (3)($1,600) = $192.40 + $4,800 = $4,992.40. 27. b. If 4 machines can complete the job in 6 hours, it will take 1 machine 4 times as long or 24 hours. It would take 3 machines 13 of 24 hrs = 13 × 24 = 8 hours. 28. d. If 16 workers take 10 days to complete a job, 1 worker would take 16 times that amount, or 160 days. It would take 8 workers 160 ÷ 8 = 20 days. Also, notice that if the amount of workers is halved, the amount of time will be doubled. 29. a. It would take 1 worker 6 × 18 = 108 days. It would take 9 workers 108 ÷ 9 = 12 days. 30. c. It would take 1 person 9 × 12 = 108 days to complete the job. It would take 36 people 3 days to complete the same job because 108 ÷ 3 = 36. 31. c. Anthony can complete 18 of the task in 1 hour. You know this because he completes the entire task in 8 hours. Together, Anthony and Elise complete 13 of the task in 1 hour. (Thus, they are done in 3 hours). Convert both fractions into twenty-fourths. 284 per hour (both) – 234 per hour (just Anthony) = 254 per hour (just Elise). Thus, Elise completes 254 of the task per hour. It will take her 245 hours to complete the entire task. 254 = 445 hours. 32. d. 40 hours of work + 60 hours of work = 100 total hours. Therefore, when considering the percent of work each did, it would be fair to give Rose 40% of the money and Marie 60% of the money. Marie gets 60% of $2,000, or 60% × $2,000 = 0.60 × $2,000 = $1,200. Alternatively, when combining their efforts, Marie and Rose earned a total of $2,000 for

–WORD PROBLEMS–

33.

34.

35.

36.

100 hours of work. This is a rate of $20 per hour. Since Marie worked 60 hours, she gets $20  60 hrs ×  hr = $1,200. c. The ratio of time spent is 18:24, which reduces to 3:4. Use this 3 to 4 ratio in the algebraic equation 3x + 4x = 7x, where 3x is the amount of money Alison gets, 4x is the amount of money Artie gets, and 7x is the total amount of money (which you know is $7,000). Thus, if 7x = $7,000, x = $1,000. Artie’s share equals 4x or (4)($1,000) = $4,000. Alternatively, you can calculate the fractional part of the job that each one worked and then use that fraction to calculate each person’s share of the contracted amount. Alison worked 18 hours and Artie worked 24 hours. The combined work time is 18 + 24 = 42 hours. This means the fractional part of the job for Alison and Artie equals 4128 and 4224 , respectively. Thus, Artie gets 4224 of the total $7,000. 4224 reduces to 74; 74 of $7,000 = $4,000, choice c. b. Tina gets paid $400 semiweekly (2 times a week) so she gets $800 per week. Multiply this weekly amount by the 4 weeks per month: $800 per week × 4 weeks per month = $3,200 per month. Jim gets paid $1,800 twice a month (semimonthly), so he gets $3,600 per month. This means Jim makes $400 more per month than Tina does. c. Ethan can type 110 reports in 6 hours, so he must type 55 reports in 3 hours. If Kayla types 60 reports and Ethan types 55 reports in 3 hours, the total number equals 115 reports. Now, compare this value with the 375 reports in the question. If they type 115 115 375  reports together in 3 hours,  3 =  x hours ; 115x 3 × 375  115 =  11 5 and x = 9.78 c. The person works a 30-hour work week for 52 weeks per year. 30 hours per week × 52

101

37.

38.

39.

40.

41.

42. 43.

weeks per year = 1,560 hours. Next, divide the total amount of money by the total amount of hours: $28,000 ÷ 1,560 = $17.95 per hour. a. Use sixteenths when considering the situation. This means 116 is coming in as 81 = 126 is going out. So every minute the net loss of fluid is 126 – 116 = 116 per minute loss. Since the tank starts out 21 full, it is 186 full. If 116 drains per minute, it will take 8 minutes for the 186 to drain. b. Pipe T fills 16 of the tank every minute. Pipe V 1 empties 4 of the tank per minute. This means the net effect every minute is 14 – 16 = 132 – 122 1 = 112 of the tank is drained. If 4 of the tank is initially full, this equals 132 full. It will take 3 minutes for these 132 to drain out at a rate of 1 1 2 per minute. b. 10,000 liters = 104 liters. Since 106 liters = 100 times 104, the number of grams of pollutant that is removed is 100 times 0.7, or 70. b. 13 gallon is lost per day over the course of a week, or 7 days. So you multiply: 13 gal per day × 7 days = 73 gal, or 213 gallons are lost. Notice that it doesn’t matter that the tank holds 14 gallons because the amount lost doesn’t come close to 14. b. Pipe A fills 110 of the tank every minute. Pipe B empties 18 of the tank per minute. This means the net effect every minute is 18 – 110 = 5 4 1 1 4 0 – 4 0 = 4 0 of the tank is drained. If 2 of the tank is initially full, this equals 2400 full. It will take 20 minutes for the 2400 to drain out at a rate of 410 per minute. a. Use the constant rate equation: D = RT. Here D = 60 kilometers × 3 hours = 180 kilometers. c. 1 kilometer = 1,000 meters. Use D = RT with 2.5 meters D =1,000, R =  seco nd , and T as the 1,000  unknown. Rearrange D = RT to T = DR =  2.5 = 400 seconds.

–WORD PROBLEMS–

44. d. Rearrange D = RT into R = DT. Substitute in the given values: R = 20 minutes = 13 hour, D = 2 miles into R = DT and R = 2 miles ÷ 13 hr = 6 miles per hour. 45. b. Sipora’s speed on the way to Stephanie’s house is irrelevant. To find the speed of her return trip, rearrange D = RT to R = D ÷ T = 220 ÷ 4 = 55 miles per hour. 46. c. Rearrange D = RT into R = D ÷ T. Amy’s rate is R = 8 miles ÷ 40 minutes = 0.2 miles per minute. Next, calculate Sharon’s rate in the same units of miles per minute. This means you need to convert the 1 hour into 60 minutes. Sharon’s rate is then R = 12 miles ÷ 60 minutes = 0.2 miles per minute. 47. b. First, convert minutes to hours: 20 minutes = 1 1  hour and 30 minutes =  hour. Next, calcu3 2 late the two distances by using D = RT. Train A will travel D = 60 × 13 = 20 miles. Train B will travel D= 55 × 12 = 27.5 miles. Thus, Train B travels the greater distance. 48. c. The first train will travel D = RT = 60 × 1 = 60 miles west. The second train will travel D = RT = 70 × 1 = 70 miles east. Thus, if the initial distance between the 2 trains was 700 miles, now the distance is 700 miles – 60 miles – 70 miles = 700 – 130 = 570 miles.

102

49. c. The total distance covered is equal to the distance that both trains travel. Train A travels east a total of D = RT = 70 × 2 = 140 miles. Train B travels west a total of D = RT = 90 × 2 = 180 miles. Note that T = 2 because the trains pass each other after 2 hours. Thus, the total initial distance is 140 miles + 180 miles = 320 miles. 50. d. The total distance will be equal to the distances traveled by both trains throughout the unknown amount of time (T). Penn Station SB Station Train 1

Train 2

D1 = 60T

D2 = 70T

initial distance apart = 260 miles = 60T + 70T

initial distance apart = 260 miles = 60T + 70T Thus, 260 = 60T + 70T = 130T, and T = 2. The trains will pass each other after two hours, so the time will be 6:00 P.M., choice d.

C H A P T E R

8

Charts, Tables, and Graphs

W

hen you pick up the newspaper or watch a news report on TV, you’ll often see information presented in a graph. More and more, you give and receive information visually. That’s one reason you’re likely to find graphs on the civil service exam, and a good reason to understand how to read them. This chapter reviews the common kinds of graphs, charts, and tables you should be familiar with before exam day. You will also review mean, median, mode, and probability—math concepts that are frequently used in chart, table, or graph questions.

103

–CHARTS, TABLES, AND GRAPHS–



Pie Charts

Pie charts show how the parts of a whole relate to one another. A pie chart is a circle divided into slices or wedges. Each slice represents a category. Pie charts are sometimes called circle graphs. Let’s look at an example of a pie chart and see what kind of information it provides. Example: The following pie chart represents data collected from a recent telephone survey. How Federal Dollars Are Spent

Other 8% Energy 10%

Space 2%

Environment Other 4% 6% Energy 11%

National Defense 2%

Health 49%

Space 12%

Environment 29%

National Defense 53%

Health 14%

How the Money Is Spent

How Voters Think the Money Should Be Spent

Using the “How Federal Dollars Are Spent” pie chart, answer the following questions. 1. 2. 3. 4.

Based on the survey, which category of spending best matches the voters’ wishes? On which category of spending did the voters want most of the money spent? Which category of spending receives the most federal dollars? To which two categories of spending did voters want the most money to go? Which two categories of spending actually received the most money? Explanations:

1. 2. 3. 4.



Energy: Voters say they would like about 10% of the budget spent on energy and about 11% is spent on energy. Health. National defense. Voters wanted money to go to health and environment. Defense and health received the most money.

Line Graphs

Line graphs show how two categories of data or information (sometimes called variables) relate to one another. The data is displayed on a grid and is presented on a scale using a horizontal and a vertical axis for the different categories of information compared on the graph. Usually, each data point is connected together to form a line so that you can

104

–CHARTS, TABLES, AND GRAPHS–

see trends in the data and so that you can see how the data changes over time. Often you will see line graphs with time on the horizontal axis. Let’s look at an example of a line graph and see the kind of information it can provide. Example: Consider the following information:

Percent of workers using each form of transportation

How People Get to Work 100 90 80 70

Public Transportation

60 50 40

Walking or Cycling

30 20 10 0

Own car 10

20

30

40

50

60

70

80

90

100 110 120 130 140 150

Population density (in workers per acre)

Using the “How People Get to Work” line graph, answer the following questions. 1. 2. 3. 4.

What variable is shown on the vertical axis? What variable is shown on the horizontal axis? As the population density increases, will more or fewer people drive their own car to work? At about what point in population density does the use of public transportation begin to level off? Which form of transportation becomes less popular as population density increases? Explanations:

1. Look at the labels. The percent of workers using each form of transportation is shown on the vertical axis. Population density is shown on the horizontal axis. 2. As population density increases, fewer people use their own cars to get to work. 3. At about 60 to 70 workers per acre, the percentage of workers using public transportation begins to level off. 4. Find the line that moves down as population density increases. It’s the line labeled “Own car.” This is the form of transportation that decreases as population density increases.



Bar Graphs

Like pie charts, bar graphs show how different categories of data relate to one another. A bar represents each category. The length of the bar represents the relative frequency of the category, compared to the other categories on the graph. Let’s look at an example of a bar graph and see the kind of information it can provide.

105

–CHARTS, TABLES, AND GRAPHS–

Example: The following bar graph compares the 2007 monthly rainfall in Cherokee County with the average monthly rainfall in Cherokee County from 2002–2006. Rainfall in Cherokee County

Title

Rainfall (in inches)

7.0

Key Monthly rainfall in 2007 Average monthly rainfall for 2002–2006

6.0 5.0 4.0 3.0 2.0 1.0 0.0 Jan

Scale

Feb

Mar

Apr

Months

May

June Bar labels

Using the “Rainfall in Cherokee County” bar graph, answer the following questions. 1. 2. 3. 4. 5.

What does each bar represent? What is the difference between the shaded bars and the white bars? During which months is the rainfall in 2007 greater than the average rainfall? During which months is the rainfall in 2007 less than the average rainfall? How many more inches of rain fell in April 2007 than in January 2007? How many more inches of rain fell in January 2007 than on average during January 2002–2006? Explanations:

1. Look at the labels and the key. Each bar represents the number of inches of rainfall during a particular month. From the key, you know that the shaded bars represent the average monthly rainfall for 2002–2006. The white bars represent the monthly rainfall in 2007. 2. Compare the white bars with the shaded bars. Rainfall in 2007 is greater than average during the months that the white bar is taller than the shaded bar for that month. Rainfall in 2007 was greater than the average rainfall during January, February, and March. 3. Compare the white bars with the shaded bars. Rainfall in 2007 is less than the average during the months that the shaded bar is taller than the white bar for that month. Rainfall in 2007 was less than the average rainfall during April, May, and June. 4. Compare the height of the white bars for January and April. In April, 6 inches of rain fell. In January, 4 inches of rain fell. Then subtract: 6 – 4 = 2. So, in April, 2 more inches of rain fell than in January. 5. Compare the height of the shaded bar and the white bar for January. The shaded bar represents 2 inches. The white bar represents 4 inches. Subtract: 4 – 2 = 2. So, two more inches of rain fell in January 2007 than on average during January 2002–2006.

106

–CHARTS, TABLES, AND GRAPHS–



Getting Information from Tables

Tables present information in rows and columns. Rows go across, or horizontally. Columns go up and down, or vertically. The box, or cell, that is made where a row and a column meet provides specific information. When looking for information in tables, it’s important to read the table title, the column headings, and the row labels so you understand all of the information. Let’s look at some examples of tables and the types of information you might expect to learn from them. Example: THE FUJITA-PEARSON TORNADO INTENSITY SCALE CLASSIFICATION

WIND SPEED (IN MILES PER HOUR)

DAMAGE

F0

72

Mild

F1

73–112

Moderate

F2

113–157

Significant

F3

158–206

Severe

F4

207–260

Devastating

F5

261–319

Cataclysmic

F6

320–379

Overwhelming

Using the “Fujita-Pearson Tornado Intensity Scale” table, answer the following questions. 1. If a tornado has a wind speed of 173 miles per hour, how would it be classified? 2. What kind of damage would you expect from a tornado having a wind speed of 300 miles per hour? 3. What wind speed would you anticipate if a tornado of F6 were reported? Explanations: 1. The wind speed for F3 tornados ranges from 158–206 miles per hour. 2. F5 tornados range in wind speed of 261–319 mph and are cataclysmic. 3. F6 tornados range from wind speeds of 320–379 miles per hour.



Statistics and Probability

Statistics is a branch of mathematics that involves the study of data. Probability is the study of chance. At times, civil service exam questions will involve charts, tables, and graphs, as well as data and chance—specifically, mean, median, mode, and probability.

107

–CHARTS, TABLES, AND GRAPHS–

When dealing with sets of numbers, there are measures used to describe the set as a whole. These are for example, called measures of central tendency and they include mean, median and mode. Mean is the average of a set of data. To calculate the mean of a set of data, add up all of the numbers in the set and divide by how many entries are in the set. If you are asked to find the mean of a set of numbers and the set is evenly spaced apart such as 2, 4, 6, 8, 10, 12, 14, the mean is the middle number in this set, because there is an odd number of data items. In this example, the mean is 8. If there is an even number of data items, there are two middle numbers: 4, 8, 12, 16, 20, and 24. In this case, the mean is the average of the two middle numbers. 12 + 16 = 28, and 28 divided by two is 14. Median is the middle value in a set of numbers that are arranged in increasing or decreasing order. If there are two middle numbers, it is the average of these two. To calculate the median of a set of numbers, first arrange the data in increasing or decreasing order. Find the middle value in a set of an odd number of entries. The median is the mean of the two middle numbers in a set of an even number of entries. Mode is the value in the set that occurs most often. There can be one mode, several modes, or no mode.

Probability is the likelihood that an event will occur. This event is called a favorable outcome, whether it is favorable to the situation or not. For example, find out the probability of rain in the forecast. If the probability of rain is 70%, then 70 out of 100 times it is expected to rain. The rain is considered a favorable outcome in this instance, even if rain is not desired. Probability of, an event is a ratio, expressed as a fraction, decimal, or percent that defines . The notation for the probability of an event is P(event). In probability problems, you can assume that all outcomes occur at random, unless otherwise noted. If the events described concern dice, assume that the dice always lands “flat” on a number. If the events concern a spinner, assume that the spinner never lands on a dividing line. Also, keep in mind: The probability of an impossible event is zero. P(impossible) = 0. The probability of an event that is certain is one. P(event that is certain) = 1. All probabilities are a number between zero and one. 0 ≤ P(event) ≤ 1. Because an event, E, will either occur or it will not occur, P(E) + P(not E) = 1.

108

–CHARTS, TABLES, AND GRAPHS–



Practice Questions

Use the following chart to answer questions 1 through 5. NAME

SCORE

Darin

95

Miguel

90

Anthony

82

Christopher

90

Samuel

88

4. What is the mode of the scores listed? a. 90 b. 89 c. 88 d. 85 5. If Anthony’s score was incorrectly reported as an 82 when his actual score on the test was a 90, which of the following statements would be true when his actual score is used in the calculations? a. The mean, median, range, and mode will change. b. The mean, median, and range, will change; the mode will remain the same. c. Only the mean and median will change. d. None of the above will ocur.

1. What is the mean score of the people listed? a. 90 b. 89 c. 88 d. 85

6. The following chart gives the times of four swimmers in their race. Which swimmer had the fastest time?

2. What is the median score of the people listed? a. 90 b. 89 c. 88 d. 85

SWIMMER

3. What is the range of the scores listed? a. 90 b. 50 c. 24 d. 13

Molly

38.51

Jeff

39.23

Asta

37.95

Risa

37.89

a. b. c. d.

109

TIME (SEC)

Molly Jeff Asta Risa

–CHARTS, TABLES, AND GRAPHS–

The table lists the number of members present at the monthly meetings for the Environmental Protection Club. MONTH

# OF MEMBERS

September

54

October

61

November

70

December

75

9. If the data presented in the table were plotted as a bar graph, which of the following represents the data most accurately? 80 a. Members attending

Use the following information to answer questions 7 through 9.

70 60 50 40 30 20 10 0

b.

c.

Dec

Sept

Oct

Nov

Dec

Sept

Oct

Nov

Dec

Sept

Oct

Nov

Dec

60 50 40 30 20 10

Members attending

80 70 60 50 40 30 20 10 0

d. Members attending

80 70 60 50 40 30 20 10 0

110

Nov

70

0

8. What was the median number of members attending during the course of the four months shown? a. 54 b. 61 c. 65.5 d. 70

Oct

80

Members attending

7. What was the average monthly attendance over the course of all the months listed? a. 71 b. 65 c. 61 d. 56

Sept

–CHARTS, TABLES, AND GRAPHS–

12. If the Johnson family budget is $4,000 per month, how much money will they save each year? a. $48,000 b. $4,800 c. $400 d. none of the above

Use the following information to answer questions 10 through 12. The pie chart shows the Johnson family’s monthly budget. Johnson Family Budget Transportation 9%

Use the following information to answer questions 13 through 16.

Clothing 4%

Savings 10%

This graph shows the yearly electricity usage for Finnigan Engineering, Inc. over the course of three years for three departments.

Housing 30% Entertainment 12%

13. The electricity cost for Sales during the year 2004 was how much greater than the electricity cost for Customer Service in 2005?

Misc. 13% Food 22%

Dollar amount consumed

1,000 900 800 700 600 500 400 300 200 100 0

10. In percent of overall expenses, how much more money is spent on food than on transportation and clothing combined? a. 9% b. 11% c. 13% d. 22%

Sales Customer Service Engineering

2004

2005 Year

a. b. c. d.

11. If the Johnson family budget is $4,000 per month, how much money is spent on housing each month? a. $800 b. $1,000 c. $1,200 d. $1,400

111

$200 $150 $100 $50

2006

2007

–CHARTS, TABLES, AND GRAPHS–

16. If the information in the bar graph associated with question 13 is transcribed and a line graph is generated, which of the following line graphs is correct? a. 1,100

14. Which of the following statements is supported by the data? a. The Sales Department showed a steady increase in the dollar amount of electricity used during the four-year period. b. The Customer Service Department showed a steady increase in the dollar amount of electricity used during the 4-year period. c. The Engineering Department showed a steady increase in the dollar amount of electricity used from 2005–2007. d. none of the above

Dollar amount consumed

1,000 900 800 700 600 500 400 300 200 100 0

Sales Customer Service Engineering

2004

2005

2006

2007

Year

b.

1,100 1,000 900 800 700 600 500 400 300 200 100 0

Dollar amount consumed

15. What was the percent decrease in electricity usage (in dollar amount) from 2004 to 2005 for the Engineering Department? a. 25% b. 20% c. 15% d. 10%

Sales Customer Service Engineering

2004

2005

2006

2007

Year 1,100 1,000 900 800 700 600 500 400 300 200 100 0

Dollar amount consumed

c.

Sales Customer Service Engineering

2004

2005

2006

2007

Year 1,100 1,000 900 800 700 600 500 400 300 200 100 0

Dollar amount consumed

d.

Sales Customer Service Engineering

2004

2005 Year

112

2006

2007

–CHARTS, TABLES, AND GRAPHS–

The table shows the numbers of male and female students involved in several school activities. ACTIVITY

MALE

FEMALE

Drama

11

13

Journalism

12

10

Science Club

9

11

Debate

12

15

Use the following chart to answer questions 20 through 23. Montgomery Inc. Yearly Profits Revenue in thousands of dollars

Use the following information to answer questions 17–19.

200

Charge Card interest

150

In-Store Purchases Online Purchases

100

50

0

2004

2005

2006

2007

Year

17. Which activity has the lowest ratio of males to females? a. Drama b. Journalism c. Science Club d. Debate 18. For all of the students listed, what percent of the students is involved in Debate? a. 15% b. 20% c. 27% d. 29% 19. If 3 more males and 4 more females join the Science Club, what percent of the students will be in this club? a. 15% b. 20% c. 27% d. 29%

113

20. Based on the chart, which answer choice represents a true statement? a. Online Purchases have increased, whereas Charge Card Interest has decreased, over the course of the four years shown. b. Charge Card Interest has increased, whereas Online Purchases have decreased, over the course of the four years shown. c. In-Store Purchases have increased, whereas Charge Card Purchases have decreased, over the course of the four years shown. d. Online Purchases have increased, whereas InStore Purchases have decreased, over the course of the four years shown.

–CHARTS, TABLES, AND GRAPHS–

21. If all of the information on the bar graph was converted into a table, which of the following tables correctly displays the data (with revenue in thousands of dollars)? a. 2004 2005 2006 2007 Charge Card $80

$90

$100

$150

$80

$90

$80

$70

$15

$60

$30

$120

22. The Online Purchases in 2004 were what fraction of the Charge Card Interest in 2007? a. 15 b. 110 c. 14 d. 12

Interest In-Store

23. In-Store Purchases in 2004 made how much more than In-Store Purchases in 2007? a. $30 b. $60 c. $6,000 d. $30,000

Purchases Online Purchases

b.

2004 2005 2006 2007

Charge Card $80

$90

$100

$120

$80

$80

$70

Use the following information to answer questions 24 through 26.

Interest In-Store

$80

The line graph shows earnings for the three divisions of Steinberg Lumber Company throughout the four quarters in 2007.

Purchases Online

$15

$60

$60

$120

c.

Revenue in thousands of dollars

Purchases

2004 2005 2006 2007

Charge Card $80

$90

$100

$150

Interest In-Store

$100

$90

$80

$70

Purchases Online

100 80 East

60

West

40

North 20 0

1st Qtr $15

$30

$60

2nd Qtr

3rd Qtr

4th Qtr

$120

Purchases

d.

24. Which of the following statements is true? a. The East Division consistently brought in more revenue than the other 2 divisions. b. The North Division consistently brought in more revenue than the West Division. c. The West Division consistently out performed the East Division. d. Both b and c are true.

2004 2005 2006 2007

Charge Card $80

$90

$100

$150

$90

$80

$80

$70

$15

$30

$60

$120

Interest In-Store Purchases Online Purchases

114

–CHARTS, TABLES, AND GRAPHS–

25. What is the percent decrease in revenue for the North Division when analyzing dollar amounts from the 3rd and 4th quarters? a. 3313% b. 40% c. 50% d. 60%

Use the following information to answer questions 27 through 29. The pie chart shows the percentage of employees in the various departments of Amelia Computer Consultants, Inc. 13%

26. During the year 2007, Steinberg Lumber secured a major contract with a developer in Canada. The East and North Divisions both supplied lumber for this project. Which of the following statements seems to be supported by the data? a. The West Division was angry that the other two divisions supplied the lumber for this contract. b. The next big contract will be covered by the West Division. c. The contract with the Canadian developer was secured in the third quarter. d. The contract with the Canadian developer was secured in the fourth quarter.

13% Customer Service

19%

Sales Tech Support Marketing

55%

27. Which two departments account for 32% of the employees? a. Marketing and Tech Support b. Customer Service and Sales c. Sales and Tech Support d. Marketing and Customer Service 28. If the total number of employees is 400, how many employees are in the Tech Support department? a. 52 b. 76 c. 110 d. 220 29. Suppose that the Customer Service department is expanded by adding 12 new employees. Which of the following statements would be true? a. Customer Service and Marketing have the same number of employees. b. The percent of employees in Marketing is now 11%. c. The percent of employees in sales is now 20%.

115

–CHARTS, TABLES, AND GRAPHS–

31. The following chart shows the cost for different categories of UTP cabling. If Athena’s office needs to buy 100 feet of UTP cable that can send data at a speed of 75 megabits per second, about how much will she spend?

d. The percent of employees in Tech Support is now 53%, while the percent of employees in Customer Service is 16%. 30. The chart shows the composition by percent of the human body with respect to various elements. ELEMENT

PERCENT BY WEIGHT

Carbon

18%

Hydrogen

10%

Oxygen

65%

Other Elements

7%

CATEGORY CHARACTERISTICS

PRICE PER FOOT

Category 1

$ 0.75

Does not support data transmission

Category 2

Supports data

$ 1.00

transmission speeds up to 4 megabits per second Category 3

For a man weighing 260 pounds, how much does the carbon in his body weigh? a. 46.8 pounds b. 48.6 pounds c. 52.4 pounds d. 54.2 pounds

Supports data

$ 1.75

transmission speeds up to 16 megabits per second Category 4

Supports data

$ 2.50

transmission speeds up to 20 megabits per second Category 5

Supports data transmission speeds up to 100 megabits per second

a. b. c. d.

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$3.00 $250 $275 $300

$ 3.00

–CHARTS, TABLES, AND GRAPHS–

33. How much did Swimming Pool World donate to the Children’s Hospital? a. $2,336.67 b. $3,651.05 c. $23,366.72 d. $36,510.50

32. During the year 2007 at Deluxe Vacuum Co., the East and West divisions had equal sales and the North sold the most. Which graph could be the graph of Deluxe’s yearly sales for 2007?

1

2 East

West

North

East

West

North

3

a. b. c. d.

34. If Swimming Pool World had pledged 1% of sales for the entire month of May, how much would they have donated? a. about $300 more b. about $300 less c. about $500 more d. about $500 less

East

West

North

East

West

North

35. The following chart shows registration for art classes for Fall 2007.

4

1 2 3 4

STUDENTS REGISTERING FOR ART CLASSES

Use the following information to answer questions 33 and 34. Swimming Pool World pledged to donate 3.2% of their sales during the second week of May to the Children’s Hospital. Here is their sales chart for May.

$5,895

Week 2

$73,021

Week 3

$54,702

Week 4

$67,891

NUMBER OF STUDENTS

Stained Glass

21

Beginning Drawing

48

Sculpture

13

Watercolors

18

TOTAL

100

If this is a representative sampling, how many out of 500 students would be expected to choose Stained Glass for their art course? a. 21 b. 92 c. 105 d. 210

MAY SALES

Week 1

COURSE

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–CHARTS, TABLES, AND GRAPHS–

Use the following information to answer questions 36 through 37.

Use the following information to answer questions 38 through 40.

The table shows the rainfall, in inches, over a 5-day period in August for Hilo, Hawaii. It also includes the total rainfall for the year and the average rainfall for a typical year.

The chart shows the colors of replacement parts for pocket PCs. The total number of parts shipped is 1,650. BOXED SET OF REPLACEMENT PARTS

RAINFALL

YEAR

NORMAL

Monday

0.08

90.88

79.15

Tuesday

0.09

90.97

79.16

Wednesday

0.70

91.67

79.17

Thursday

0.19

91.86

79.17

Friday

0.32

92.18

79.50

PART COLOR

NUMBER OF PIECES

Green

430

Red

425

Blue

36. Find the average rainfall for the 5-day period in August. a. 1.38 inches b. 0.276 inches c. 0.32 inches d. 0.237 inches

Yellow

345

TOTAL

1,650

38. If a person randomly grabbed a part out of the box, what is the probability that the part would be blue? a. 14 b. 19 c. 112 d. 131

37. Using Monday’s reading and rounding off to the nearest whole percent, the year-to-date record is what percent of the normal reading? a. 13% b. 15% c. 87% d. 115%

39. Approximately what percent of the total shipment is red? a. 18% b. 20% c. 26% d. 30%

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–CHARTS, TABLES, AND GRAPHS–

41. The area of the smallest lot listed is approximately what percent of the area of the largest lot listed? a. 25% b. 50% c. 75% d. 85%

40. If the following chart shows the number of replacement parts that were found to be defective, what percent of the new parts is defective? BOXED SET OF REPLACEMENT PARTS PART COLOR

NUMBER OF DEFECTIVE PIECES

Green

14

Red

10

Blue

8

Yellow

12

a. b. c. d.

42. How much land does Mr. Taylor own in the Orange Grove subdivision? a. 23,066 sq. ft b. 29,765 sq. ft c. 31,950 sq. ft d. 32,070 sq. ft

2213% 18% 812% 223%

Use the following information to answer questions 41 through 43. The table lists the size of building lots in the Orange Grove subdivision and the people who are planning to build on those lots. For each lot, installation of utilities costs $12,516. The city charges impact fees of $3,879 per lot. There are also development fees of 16.15 cents per square foot of land. LOT

AREA (SQ. FT.)

BUILDER

A

8,023

Ira Taylor

B

6,699

Alexis Funes

C

9,004

Ira Taylor

D

8,900

Mark Smith

E

8,301

Alexis Funes

F

8,269

Ira Taylor

G

6,774

Ira Taylor

43. How much will Mr. Smith pay in development fees for his lot? a. $1,157.00 b. $1,437.35 c. $143,735 d. $274,550 44. Felipe is planning to get wireless Internet service at his house. Two service providers, A and B, offer different rates as shown in the table below. If Felipe plans on using 25 hours of Internet service per month, which of the following statements is true? INTERNET SERVICE RATES PROVIDER

FREE HOURS

BASE CHARGE

HOURLY CHARGE

A

17.5

$ 20.00

$ 1.00

B

20

$20.00

$1.50

a. b. c. d.

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Provider A will be cheaper. Provider B will be cheaper. The providers will cost the same per month. The answer cannot be determined from the information given.

–CHARTS, TABLES, AND GRAPHS–

P wave

45. Refer to the following table to answer this question. If you take recyclables to the recycler who will pay the most, what is the most money you could get for 2,200 pounds of aluminum, 1,400 pounds of cardboard, 3,100 pounds of glass, and 900 pounds of plastic? RECYCLER ALUMINUM CARDBOARD GLASS

PLASTIC

X

Y

a. b. c. d.

$.06/

$.03/

$.07/

$.02/

pound

pound

pound

pound

$.07/

$.04/

$.08/

$.03/

pound

pound

pound

pound

S wave

Travel Time (minutes)

25

WEIGHT (OZ.)

W

0.21

6

X

0.48

15

Y

0.56

20

Z

0.96

32

10

5

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

Distance from Epicenter (kilometers)

47. How many minutes does it take the S wave to travel 5,500 kilometers? a. 15 minutes b. 20 minutes c. 25 minutes d. 30 minutes 48. Approximately how many minutes does it take a P wave to travel 8,000 km? a. 6 minutes b. 12 minutes c. 3 minutes d. 15 minutes

46. Which of the following brands is the least expensive per ounce? PRICE ($)

15

0

$409 $440 $447 $485

BRAND

20

49. An earthquake occurs at noon, and the recording station receives the S wave at 12:04 P.M. How far away is the earthquake? a. 1,000 kilometers b. 2,000 kilometers c. 3,000 kilometers d. 4,000 kilometers

a. W b. X c. Y d. Z Use the following information to answer questions 47 through 50. When an earthquake occurs, some of the energy released travels through the ground as waves. Two general types of waves are generated. One type is called the P wave, and the other is called the S wave. A graph can be made of the travel times of these waves.

50. How far away is an earthquake if the difference in arrival time between the P and S waves is 5 minutes? a. 1,000 kilometers b. 3,000 kilometers c. 4,000 kilometers d. 7,000 kilometers

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–CHARTS, TABLES, AND GRAPHS–



Answers

1. b. The formula for calculating the mean (average) is: sum of all values Mean =  # of values The sum of all the values given is: 95 + 90 + 82 + 90 + 88 = 445. The number of values 445  (scores) is 5. Thus, the mean =  5 = 89. 2. a. First, list all of the scores in order: 82, 88, 90, 90, 95. The middle score will be the median, thus 90 is the median. 3. d. The range is calculated by subtracting the lowest score from the highest score. Thus, the range is 95 – 82 = 13. 4. a. The mode is the score that occurs the most. Here, there are two 90s, thus 90 is the mode. 5. d. Calculate the new median, mode, and range and compare them to the original values. To find the new mean, first add all the scores: 95 + 90 + 90 + 90 + 88 = 453, and then divide by 5: 453 ÷ 5 = 90.6. Next, you can calculate the median and see if it is different: 88, 90, 90, 90, 95. Here you see that the median is the same as it was before, 90. The mode is still 90 because 90 is the score that occurs the most. The range is now 95 – 88 = 7. Thus, choice d is the correct answer. 6. d. The fastest swimmer will have the quickest time. 37.89 is the fastest. Thus, Risa is the fastest swimmer. 7. b. The formula for calculating the mean (average) is: sum of all values  Mean =  # of values The sum of all the values given is: 54 + 61 + 70 + 75 = 260. The number of values is 4. Thus, the mean = 260 ÷ 4 = 65. 8. c. List all of the values in order: 54, 61, 70, 75. Here, there is an even number of values, so

121

9.

10.

11.

12.

13.

14.

15.

you average the middle 2 numbers. The aver131  age of 61 and 70 is  2 = 65.5. b. The number of members attending for the four months was: 54, 61, 70, 75, for September, October, November, and December, respectively. This is accurately displayed in choice b. Note that choice b is also the only choice that depicts the ascending trend. That is to say, the number of members in attendance increases over time. a. 22% is spent on food. When you combine transportation (9%) and clothing (4%), the sum is 13%. Thus, the amount spent on food is 22% – 13% = 9% greater. c. Housing is 30% of the monthly budget. 30% of $4,000 is calculated by multiplying: 30% × $4,000 = 0.30 × $4,000 = $1,200. b. They save 10% of $4,000 each month: 0.10 × $4,000 = $400. Over the course of a year they will save $400 per month × 12 months = $4,800. d. The Sales Dept (black bar) spent $750 on electricity in 2004. The Customer Service Dept (lightest bar) spent $700 on electricity in 2005. Thus, the Sales Dept spent $750 – $700 = $50 more. c. The usage for the Engineering Department increases by $100 each year from 2005 through 2007. None of the other statements are supported by the data. Claims of steady increase over the course of four years would be represented as four bars, each with a greater height than the previous one. b. The difference in dollar amounts used is $1,000 – $800 = 200. When compared with the original $1,000 consumed, this can be expressed as a 200 x percent by equating  1,0 00 =  10 0 . Thus, x = 20%.

–CHARTS, TABLES, AND GRAPHS–

16. d. The line graph in choice d accurately displays the data that is obtained from the bar graph. 17. d. The M:F (male to female) ratios are as follows: Drama: 1113 ≈ 0.85 Journalism: 1120 = 1.2 Science Club 191 ≈ 0.82 Debate 1125 = 0.8 Here, 0.8 is the least value, so a 1125 ratio is the smallest M:F ratio listed. 18. d. This question is solved by adding a column and row labeled “Total” onto the side and bottom of the given chart: ACTIVITY

MALE

FEMALE

TOTAL

Drama

11

13

24

Journalism

12

10

22

Science Club

9

11

20

Debate

12

15

27

TOTAL

93

Now you can see that 27 students out of the 93 total are involved in Debate. 2973 ≈ 0.29. To write these values as a percent, move the decimal point two places to the right and add the percent symbol: 29%. 19. c. Using the new information, our chart becomes: ACTIVITY

MALE

FEMALE

TOTAL

Drama

11

13

24

Journalism

12

10

22

Science Club

12

15

27

Debate

12

15

27

TOTAL

100

This means that 27 out of 100 students are 27 now in the Science Club.  10 0 = 27%.

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20. d. The black bars (Charge Card) increase from year to year. The lightest bars (In-Store Purchases) decrease from year to year. The gray bars (Online Purchases) increase from year to year. Thus, only choice d is correct. 21. c. The black bars (Charge Card) increase from 80 to 90 to 100 to 150. The lightest bars (InStore Purchases) decrease from 100 to 90 to 80 to 70. The gray bars (Online Purchases) increase from 15 to 30 to 60 to 120. Only choice c presents this data correctly. 22. b. In 2004, Online Purchases were at $15,000. In 2007, Chard Card Interest totaled $150,000. Since 15 is 110 of 150, the answer is 110 , choice b. 23. d. Note that all dollar amounts in the chart are expressed as “Revenue in thousands of dollars.” In 2004, the In-Store Purchases were at $100,000. In 2007, the amount is $70,000. Thus, the difference is $30,000. Thus, choice d, $30,000, is correct. 24. b. Looking at the graph, you see that the line for North (the line with triangular points) is always higher than the line for West (the line with the square points). All other statements are not supported by the data in the graph. Thus, only choice b is true. 25. a. Here the revenue in thousand of dollars decreases from 60 to 40. Thus, the difference is 20. As compared with the original 60, this represents 2600 = 0.333 . . . To express this as a percent, just move the decimal point 2 places to the right: 0.3333 → 3313%. 26. c. Since you are told that this was a “major” contract, the statement best supported by the data is choice c: “The contract with the Canadian developer was secured in the third quarter.” The data supports this statement because both the East and North Divisions had a sig-

–CHARTS, TABLES, AND GRAPHS–

27.

28.

29.

30. 31.

nificant revenue increase during the third quarter, which might be indicative of having a large contract for that quarter. b. Customer Service (black) accounts are 13% of the total, and Sales (dark gray) accounts are 19% of the total. Together these add to 32%. Since both Marketing and Customer Service are at 13%, either department could be combined with Sales to total 32% of the company employees. Note that only Customer Service and Sales are listed as a choice. d. Tech Support (the lightest) is 55% of the total. 55% of 400 equals 55% × 400 = 0.55 × 400 = 220. You can save time when answering a question like this by noticing that 55% will be slightly more than 21 the total of 400, so slightly more that 200. Only choice d is correct. d. Before the addition of the 12 new customer service representatives, the number of employees in each department was as follows: Customer Service: 0.13 × 400 = 52 Marketing: 0.13 × 400 = 52 Sales: 0.19 × 400 = 76 Tech Support: 0.55 × 400 = 220 The new total is 400 + 12 = 412. The new number of customer service employees is 52 + 12 = 64. The percentages are as follows: 64 Customer Service:  41 2 ≈ 0.15534 ≈ 15.5 % ≈ 16% 52 Marketing:  41 2 ≈ 0.12621 ≈ 12.6% ≈ 13% 76 Sales:  41 2 ≈ 0.18447 ≈ 18.4% ≈ 18% 200  Tech Support:  412 ≈ 0.53398 ≈ 53.4% ≈ 53% Thus, the only choice that would be true is choice d. a. Carbon accounts for 18% of body weight. 18% of 260 = 0.18 × 260 = 46.8 pounds. d. Since she needs to support a speed of 75 megabits per second, only Category 5 UTP cable can be used. Note that Category 5 “Sup-

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32.

33.

34.

35.

36.

37.

ports data transmission speeds up to 100 megabits per second.” This cable costs $3 per foot, so 100 feet will cost 100 × $3.00 = $300. d. The East and West divisions had equal sales, so you need a graph where the bars for East and West are the same height. North sold the most, so you need a graph that also shows North as having the largest bar in the graph. Graph 4 shows this situation. Thus, choice d is correct. a. During Week 2, they made $73,021. To find 3.2% of this amount, multiply by 0.032: 0.032 × $73,021 = $2,336.672. Rounded to the nearest cent, the answer is $2,336.67. b. First, calculate the total by adding up all the dollar amounts: $5,895 $73,021 $54,702 + $67,891 $201,509 Next, take 1% of the total by multiplying by 0.01; 0.01 × $201,509 = $2,015.09. This is about $300 less than the $2,336.67 that they actually donated. c. Since the sampling is representative, this means that the same trend will be seen when a larger sample is considered. Thus, multiply by 5 to see how many students out of 500 will choose stained glass. 5 × 21 = 105. b. Add up the values for the 5 days shown: 0.08 + 0.09 + 0.70 + 0.19 + 0.32 = 1.38. Divide this amount by 5 to get the average: 1.38 ÷ 5 = 0.276 inches. d. On Monday, the year to date is 90.88 inches. The normal amount is 79.15. Thus, the yearto-date value is above 100% of the normal value, making choice d the only possible cor90.18  rect answer. (Note that  79.15 ≈ 1.1482 ≈ 114.82% ≈ 15%.)

–CHARTS, TABLES, AND GRAPHS–

38. d. 430 + 425 + 345 = 1,200 parts are accounted for. Since the total is 1,650; 1,650 – 1,200 = 450 blue parts. When randomly picking a part, the chance of getting blue is 450 out of 450 450  1,650 =  1,6 50 . Simplify the expression: 1,650 ÷ 3 150  = 1 1. 150 450 39. c. 425 out of 1,650 is red.  1,6 50 = 425 ÷ 1,650 = 0.25757. To convert to a percent, move the decimal point two places to the right and add the percent symbol: 25.7575 . . . % ≈ 26%. 40. d. Add a row for the total at the bottom of the given chart: BOXED SET OF

NUMBER OF DEFECTIVE PIECES

Green

14

Red

10

Blue

8

Yellow

12

TOTAL defective

44

LOT

AREA (SQ. FT.)

BUILDER

A

8,023

Ira Taylor

B

6,699

Alexis Funes

C

9,004

Ira Taylor

D

8,900

Mark Smith

E

8,301

Alexis Funes

F

8,269

Ira Taylor

G

6,774

Ira Taylor

The total amount of land he owns is 8,023 + 9,004 + 8,269 + 6,774 = 32,070 square feet. 43. b. Mr. Smith’s lot is 8,900 square feet. You are told “There are also development fees of 16.15 cents per square foot of land.” 16.15 cents = $0.1615. Thus, he must pay $0.1615 × 8,900 = $1,437.35 in development fees. 44. c. When used for 25 hours per month, Provider A will cost $20 + 7.5 × $1 (for the hourly charge above the free hours). This equals $27.50. Provider B will cost $20 plus 5 × $1.50 (for the hourly charge above the free hours). This equals $20 + $7.50 = $27.50 as well, so choice c is the correct answer. 45. d. Since Recycler Y pays more per pound for all four types of recyclables, all four items should be brought there. The aluminum will yield 0.07 × 2,200 = $154. The cardboard will yield 0.04 × 1,400 = $56. The glass will yield 0.08 × 3,100 = $248. The plastic will yield 0.03 × 900 = $27. These add to $485.

REPLACEMENT PART PART COLOR

42. d. Look at the chart to see all of the land he owns:

44 44 parts out of 1,650 are defective.  1,6 50 = 0.02666. To express this as a percent, move the decimal point two places to the right and add the percent symbol: 2.66666 . . . %. This equals 223%. 41. c. The smallest lot is 6,699 square feet and the largest lot is 9,004 square feet. 6,699 out of 6,699  9,004 =  9,004 ≈ 0.74400 ≈ 74.40% ≈ 74%. Thus, choice c, 75% is the best approximation.

124

–CHARTS, TABLES, AND GRAPHS–

46. c. Calculate the price per ounce (oz.) for each brand: .21  = 0.035 W: 6 .48  = 0.032 X: 15 .56  = 0.028 Y: 20 .96  = 0.03 Z: 32 Thus, brand Y is the least expensive, choice c. 47. a. The solid line represents the S wave. This crosses 550 kilometers at time = 15 minutes.

earthquake is 1,000 kilometers away. P wave S wave

Travel Time (minutes)

25

Travel Time (minutes)

5

1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000

50. b. A difference in time of 5 minutes can be seen by looking at the vertical axis. The vertical axis is marked by 5-minute intervals, so use this distance to judge where the distance (gap) between the waves is also 5 minutes. Look down to see the horizontal axis to note that this time difference occurs at 3,000 kilometers.

S wave

20

15

10

5

1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000

Distance from Epicenter (kilometers)

48. b. The P wave is the dashed line. It travels 8,000 kilometers at a point above time = 10, but below time = 15. Hence, a time of 12 minutes is the best answer.

P wave S wave

Travel Time (minutes)

25

P wave S wave 25

Travel Time (minutes)

10

Distance from Epicenter (kilometers)

25

20

20

15

10

5

0

1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000

Distance from Epicenter (kilometers)

15

10

5

0

15

0

P wave

0

20

1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000

Distance from Epicenter (kilometers)

49. a. The S wave was received 4 minutes after the earthquake. Locate 4 minutes on the vertical axis of the graph and then move across until you reach the S-wave graph. Look down to the horizontal axis to see that this means the

125

C H A P T E R

9

Measurement and Geometry

I

n the metric system, lengths are calculated in meters, masses are calculated in grams, and volumes are calculated in liters. The prefix of each unit is very important. You should be familiar with the following prefixes:

PREFIX

MEANING

EXAMPLE

milli

1  1,0 00

1 1 milligram is  1,0 00 of a gram.

centi

1   100

deci

1  1 0

of

1 decigram is 11 0 of a gram.

deca

10 times

1 decameter is 10 meters.

hecto

100 times

1 hectoliter is 100 liters.

kilo

1,000 times

1 kilometer is 1,000 meters.

of

of

1  of a meter. 1 centimeter is  100

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–MEASUREMENT AND GEOMETRY–



English Units

The relationships between the English, or customary, units are not as systematic as the relationships between units in the metric system. Here, lengths are measured in inches, feet, yards, and miles. Weights are measured in pounds and ounces. And volumes are measured in cubic inches, cubic feet, and so forth. Here is a chart of common conversions for English units. COMMON CONVERSIONS



1 foot = 12 inches

1 cup = 8 fluid ounces

3 feet = 1 yard

1 pint = 2 cups

1 mile = 5,280 feet

1 quart = 2 pints

1 acre = 43,560 square feet

1 gallon = 4 quarts

1 ton = 2,000 pounds

1 pound = 16 ounces

1 gross = 144 units

1 liter = 1,000 cubic centimeters

Converting Units

Conversion factors are an easy way to convert units. For example, using the knowledge that 12 inches = 1 foot, 1 ft. 12 in.   you can generate two conversion factors:  1 ft. and 12 in. Suppose you wanted to convert 5 feet into inches. You 12 in.  can use the conversion factor  1 ft. : 12 in.  = 60 in. 5 ft. ×  1 f t.

Notice that you crossed out the units you didn’t want (feet) and ended up with the units you did want (inches). Having the feet in the denominator of this conversion factor lets us cross out the “ft.” unit in the original 5 feet. In other instances, you may want to cross out inches and convert to feet. The conversion factor to use 1 ft.  would be  12 in. .



Calculations with Geometric Figures

Perimeter is the distance around a figure. The perimeter of a circle is called its circumference. Area is a measure of the surface of a two-dimensional figure. Volume is a measure of the amount of space inside a three-dimensional shape.

128

Formula Sheet You should be familiar with the formulas presented on

Parallelogram: Area = bh, where b stands for base

this formula sheet.

and h stands for height.

Triangle: Area = 12bh, where b stands for base and h h

stands for height. h

b b

Trapezoid: Area =

1 2h(b 1

+ b2), where h stands for

height and b stands for base.

The interior angles of a triangle add to 180°.

b2

The interior angles of a quadrilateral (4-sided polygon) add to 360°.

h

Square: Area = s2, where s stands for side. b1 s

Pythagorean theorem: a2 + b2 = c2, where a and b are legs and c is the hypotenuse.

Perimeter = 4s

c

b

Rectangle: Area = lw, where l stands for length and w a

stands for width.

Right circular cylinder: Volume = r2h, where r stands w

for radius and h stands for height. r

l h

Circle: Area =  r2, where r stands for radius.

r

Total Surface Area = 2πrh + 2πr2 Rectangular solid: Volume = lwh, where l stands for length, w stands for width, and h stands for height. Circumference = 2r = d, where d stands for diameter.

l

( ≈ 3.14 or 272)

w h

Total Surface Area = 2(lw) + 2(hw) + 2(lh)

129

–MEASUREMENT AND GEOMETRY–



Perimeter

Perimeter is an addition concept. It is a linear, one-dimensional measurement of the distance around the outside of a figure. To find perimeter, add up all the lengths of the sides of the figure. Then, name the units. Be alert when working with geometry problems to make sure that the units are consistent. If they are different, a conversion must be made before calculating perimeter.



Area

Area is a measure of how many square units it takes to cover a closed figure. Area is measured in square units. Area is a multiplication concept, where two measures are multiplied together. You can also think of units being multiplied together: cm × cm = cm2, or the words “centimeters squared.” Let’s look at an example involving area: Example: A rectangular swimming pool measures 204 feet long and 99 feet wide. What is the area of the pool in square yards? Convert both the length and the width into yards: 1 yd.  204 ft. ×  3 ft. = 68 yd. 1 yd.  99 ft. ×  3 ft. = 33 yd.

Next, use the area formula for a rectangle, A = lw: A = 68 yards × 33 yards = 2,244 square yards.



Volume

Volume is a measure of how many cubic units it takes to fill a solid figure. Volume is measured in cubic units. Volume is a multiplication concept, where three measures are multiplied together. Example: One cubic centimeter of wood weighs 6 grams. How much would a cube weigh if it measured 10 centimeters on each side? 6g 3 You are told that the weight is 6 grams per cubic centimeter, or  cm3 . You need to find out how many cm there are in the bigger cube, which is the volume of the cube. Recall that for a cube, V = side3. The bigger cube 6g has a side = 10, so V = 103 = 1,000 cm3. Then, to find the weight, you multiply 1,000 cm3 ×  cm3 = 6,000 grams.

130

–MEASUREMENT AND GEOMETRY–



Practice Questions

b. 20 yards 1 foot c. 21 yards 1 foot d. 21 yards 12 foot

1. What is the sum of 3 feet 5 inches, 10 feet 2 inches, and 2 feet 7 inches? a. 14 feet 14 inches b. 16 feet 4 inches c. 15 feet 13 inches d. 16 feet 2 inches

7. How many yards are in a mile? a. 1,760 b. 4,400 c. 5,280 d. 63,360

2. Three pieces of pipe measure 5 feet 8 inches, 4 feet 7 inches, and 3 feet 9 inches. What is the combined length of all three pipes? a. 14 feet b. 13 feet 10 inches c. 12 feet 9 inches d. 12 feet 5 inches

Use the following chart to answer questions 8 through 10. ENGLISH—METRIC UNIT CONVERSIONS LENGTH

1 in. = 2.54 cm 1 yard = .9 m

3. How many inches are there in 313 yards? a. 126 b. 120 c. 160 d. 168

1 mi. = 1.6 km

4. 76,000 milliliters is equivalent to how many liters? a. 7.6 liters b. 76 liters c. 760 liters d. 7,600 liters 5. 2,808 inches is equivalent to how many yards? a. 234 b. 110 c. 78 d. 36

8. Convert 3 feet 5 inches into centimeters. a. 104.14 centimeters b. 65.6 centimeters c. 51.3 centimeters d. 16.14 centimeters 9. 5,500 yards is equivalent to how many meters? a. 13,970 meters b. 6,111 meters c. 9,800 meters d. 4,950 meters 10. 1,280 miles is equal to how many kilometers? a. 800 kilometers b. 1,152 kilometers c. 2,048 kilometers d. 3,200 kilometers

6. What is the sum of 5 yards 2 feet, 8 yards 1 foot, 3 yards 12 foot, and 4 yards 6 inches? a. 20 yards 12 foot

131

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15. 364 ounces is equivalent to how many quarts? a. 182 quarts b. 91 quarts c. 22.75 quarts d. 11.375 quarts

11. A child has a temperature of 40 degrees C. What is the child’s temperature in degrees Fahrenheit? F = 95C + 32 a. 101º b. 102º c. 103º d. 104º 12. If John was waiting for 45 minutes for an appointment with a contractor that lasted 1 hour and 25 minutes, what is the total amount of time spent at the contractor’s office? a. 2 hour 10 minutes b. 2 hour 25 minutes c. 212 hours d. 3 hour 10 minutes 13. There are 12 yards of twine on a roll. Danielle cuts off 2 feet of twine for a project. How many feet of twine are left on the roll? a. 2 b. 34 c. 36 d. 142 Use the following conversion chart to answer questions 14 through 17.

16. How many ounces are in 3 gallons? a. 384 ounces b. 192 ounces c. 96 ounces d. 48 ounces 17. A 25-gallon tub of fluid will be poured into containers that hold half of a quart each. If all of the containers are filled to capacity, how many will be filled? a. 50 b. 100 c. 200 d. 250 18. A rotating door, pictured here, has four sections, labeled a, b, c, and d. If section a is making a 45 degree angle with wall 1, what angle is section c making with wall 2? (Note: Wall 1 and wall 2 are segments of the same line.)

LIQUID MEASURE

d

c

1

2

8 oz. = 1 c.

a

1 pt. = 2 c.

a. b. c. d.

1 qt. = 2 pt. 4 qt. = 1 gal.

14. How many ounces are in 2 pints? a. 16 ounces b. 32 ounces c. 44 ounces d. 64 ounces 132

15 degrees 45 degrees 55 degrees 90 degrees

b

–MEASUREMENT AND GEOMETRY–

19. A rectangle has 2 sides equaling 6 feet and 1 yard, respectively. What is the area of the rectangle? a. 6 square feet b. 12 square feet c. 18 square feet d. 20 square feet

24. A rectangular swimming pool measures 160 feet long and 80 feet wide. What is the perimeter of the pool in yards? a. 480 b. 160 c. 240 d. 280

20. A square with s = 6 centimeters has the same area of a rectangle with l = 9 centimeters. What is the width of the rectangle? a. 4 centimeters b. 6 centimeters c. 8 centimeters d. 9 centimeters

25. In the diagram, the angle x equals how many degrees? 40°

x

21. If the area of a circle is 9 square centimeters, what is the circumference? a. 3 square centimeters b. 3 centimeters c. 6 square centimeters d. 6 centimeters 22. A rectangular tract of land measures 860 feet by 560 feet. Approximately how many acres is this? (1 acre = 43,560 square feet.) a. 12.8 acres b. 11.06 acres c. 10.5 acres d. 8.06 acres

a. b. c. d.

70° 110° 140° 290°

26. If the volume of a cube is 8 cubic inches, what is its surface area? a. 80 square inches b. 40 square inches c. 24 square inches d. 16 square inches

23. Marguerite is redoing her bathroom floor. Each imported tile measures 127 inches by 145inches What is the area of each tile? a. 1385 square inches 11 b. 1 13 5 square inches 11 c. 235 square inches d. 3335 square inches

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30. What is the area of the polygon? a. 8 square units b. 12 square units c. 20 square units d. 24 square units

27. Giorgio is making an “open” box. He starts with a 10 × 7 rectangle, then cuts 2 × 2 squares out of each corner. To finish, he folds each side up to make the box. What is the box’s volume? 10

31. The standard distance of a marathon is 26.2 miles. If the length of a walker’s stride is 1.96 feet, approximately how many steps does this walker take to walk a marathon?

7 2

a. b. c. d.

36 units3 42 units3 70 units3 72 units3

28. How many six-inch square tiles are needed to tile the floor in a room that is 12 feet by 15 feet? a. 180 tiles b. 225 tiles c. 360 tiles d. 720 tiles Refer to the following polygon to answer questions 29 and 30.

1.96 ft.

a. b. c. d.

23,527 70,580 138,336 271,139

32. What is the measure of angle C in the triangle?

2 2 2 C 2 2

a. b. c. d.

2

29. What is the perimeter of the polygon? a. 8 units b. 12 units c. 20 units d. 24 units

134

90° 60° 45° 25°

–MEASUREMENT AND GEOMETRY–

33. How much greater is the area of circle B? B A

5 3

a. b. c. d.

16 square inches 9 square inches 25 square inches 14 square inches

36. One cubic centimeter of clay weighs 3 grams. How much would a cube weigh if it measured 5 centimeters on each side? a. 15 grams b. 125 grams c. 375 grams d. 75 grams Use the following information and diagram to answer questions 37–39. A

34. ABCD is a square and E is the midpoint of  AB . Find the area of the shaded region. A

E

B

B

24

C

4

A

D

a. b. c. d.

5

C

4 square units 6 square units 8 square units 12 square units

B

Note: All of the sides of ABC are half the value of the corresponding sides of ABC.

35. Two angles in quadrilateral ABCD have their measures indicated. The other two angles show variable expressions. What is x? A 100°

90° D

a. b. c. d.

50° 60° 70° 80°

C

B (2x° + 20)

x° C

37. Calculate the length of side AC in triangle ABC. a. 10 b. 12 c. 13 d. 26 38. The perimeter of ABC is how much greater than the perimeter of ABC? a. 30 b. 40 c. 45 d. 60

135

–MEASUREMENT AND GEOMETRY–

39. The area of ABC is how much greater than the area of ABC? a. 30 b. 40 c. 60 d. 90

42. What is the area of the shaded part of the circle if the diameter is 6 inches? (Use 3.14 for .)

60°

d=6

40. What is the value of X in the following figure? a. b. c. d.

10 1

X

a. b. c. d.

3 4 5 6

41. Find the area of the shaded portion in the figure.

4.71 square inches 28.26 square inches 60 square inches 36 square inches

43. A cylindrical can measures 4.2 inches in height. Its circular bases of 21 inch radii are removed, and the cylinder is flattened out. What is the surface area of the flattened-out cylinder? (Use 3.14 for .) a. 3.297 square inches b. 8.54 square inches c. 12.1 square inches d. 13.188 square inches

r=1

a. b. c. d.

 –1 2– 4–

44. A point on the outer edge of a wheel is 2.5 feet from the axis of rotation. If the wheel spins at a full rate of 2,640 revolutions per minute, how many miles will the point on the outer edge of the wheel travel in one hour? a. 75 b. 100 c. 112 d. 150

136

–MEASUREMENT AND GEOMETRY–

48. A triangle has sides that are consecutive even integers. The perimeter of the triangle is 24 inches. What is the length of the shortest side? a. 10 inches b. 8 inches c. 6 inches d. 4 inches

45. What is the perimeter of the shaded area if the shape is a quarter-circle with a radius of 3.5? (Use  = 272 .)

a. b. c. d.

7 units 11 units 22 units 29 units

49. In the following diagram, a circle with an area of 100 square inches is inscribed in a square. What is the length of A B ?

46. In the diagram, a half-circle is laid adjacent to a triangle. What is the total area of the shape, if the radius of the half-circle is 3 and the height of the triangle is 4?

47. What is the area of the following shaded triangle?

D

C

10 inches 20 inches 40 inches 100 inches

50. A bike wheel has a radius of 12 inches. How many revolutions will it take to cover 1 mile? (Use 1 mile = 5,280 feet, and ( = 272 .) a. 70 b. 84 c. 120 d. 840

10

a. b. c. d.

B

a. b. c. d.

a. 6( + 4) b. 6 + 12 c. 6 + 24 d. 92 + 12

5

A

6

20 square units 25 square units 40 square units 44 square units

137

–MEASUREMENT AND GEOMETRY–



Answers

1. d. First, add up all of the given values: 3 ft. 5 in. 10 ft. 2 in. + 2 ft. 7 in. 15 ft. 14 in. Next, note that 14 inches = 1 foot + 2 inches. This means 15 feet 14 inches = 16 feet 2 inches, choice d. 2. a. First, add up all of the given values: 5 ft. 8 in. 4 ft. 7 in. + 3 ft. 9 in. 12 ft. 24 in. Next, note that 24 inches = 2 feet, so 12 feet 24 inches is equivalent to 14 feet. 3. b. Since there are 36 inches per yard, use the con36 in. 1 36 in.   version factor  1 yd. , and multiply: 33 yd. ×  1 yd. 10 36 in. 360   = 3 yd. ×  1 yd. = 3 inches. = 120 inches. 4. b. 1 liter = 1,000 milliliters so you can use the 1L  conversion factor  1,000 ml to convert the milli1L  liters into liters. 76,000 ml ×  1,000 ml = 76 L. 5. c. Since there are 36 inches per yard, use the 1 yd. conversion factor  36  in. and multiply: 1 yd. 2,808 in. ×  36  in. = 78 yd.

7. a. 1 mile equals 5,280 feet (memorize this). Since there are 3 feet per yard, use the conver1 yd. 1 yd.   sion factor  3 ft. and multiply: 5,280 feet × 3 ft. = 1,760 yards. 8. a. First, convert 3 feet 5 inches into 36 inches + 5 inches = 41 inches. Next, use the information given in the chart to make a conversion factor. Since 1 inch = 2.54 centimeters, and you want to end up with centimeters, you make a conversion factor with inches in the 2.54 cm  denominator:  1 in. Next, multiply: 41 2.54 cm  inches ×  1 in. = 104.14 centimeters. 9. d. The chart shows that 1 yard = .9 meters, so .9 m you can write the conversion factor as  1 y d. .9 m  and multiply: 5,500 yd. ×  = 4,950 meters. 1 yd. 10. c. The chart shows that 1 mile = 1.6 kilometers, so you can write the conversion factor as 1.6 km 1.6 km  and multiply: 1,280 miles ×  = 1 mi. 1 mi. 2,048 kilometers. 11. d. Substitute 40 in for C in the given equation. Thus, (F = 95 C + 32) becomes F = 95(40) + 32 = (9)(8) + 32 = 72 + 32 = 104 degrees Fahrenheit. 12. a. Line up the units and add: 45 min + 1 hr 25 min 1 hr 70 min Next, note that 70 minutes = 1 hour 10 minutes. Thus, 1 hour 70 minutes = 2 hour 10 minutes. 13. b. First convert the 12 yards into feet: 12 yd. × 3 ft.  1 y d. = 36 feet at the start. Next, Danielle cuts 2 feet off, so 34 feet are left. 14. b. Using the chart, you can make conversion factors where you will cross off pints and end up with ounces (oz). Thus, you multiply: 2 8 oz. 2 c. pints ×  1 p t. ×  1 c. = 32 ounces.

6. c. First, note that 4 yards 6 inches is the same as 4 yards 12 foot, as this will help you combine units. Next, add up all the values: 5 yd. 2 ft. 8 yd. 1 ft. 3 yd. 12 ft. 1

+ 4 yd. 2 ft. 20 yd. 4 ft. Next, note that 4 feet = 1 yard + 1 foot. Thus, 20 yards 4 feet can be converted to 21 yards 1 foot.

138

–MEASUREMENT AND GEOMETRY–

15. d. Using the chart, you can make conversion factors where you will cross off ounces (oz) and 1 c. 1 pt.  end up with quarts (qt): 364 ounces ×  8 o z. ×  2 c. 1 qt. 364  × 2 p t. =  32 = 11.375 quarts. 16. a. Using the chart you can make conversion factors where you will cross off gallons and end 4 qt. 2 pt.  up with ounces (oz): 3 gallons ×  1 g al. ×  1 qt. × 2 c. 8 oz.   1 p t. ×  1 c. = 384 ounces. 17. c. First, convert the gallons into quarts: 25 4 qt. gallons ×  1 g al. = 100 qt. If the fluid will fill 100 one-quart containers, it will then fill 200 1 -quart containers. 2 18. b. If you draw a line on the diagram to denote the 45° angle mentioned, you can see that the angle section c makes with wall 2 must also be 45°. Recall that opposite angles formed by the intersection of two straight lines are equal: d

24.

25.

2

45° a

23.

c 45°

1

22.

b

This means that section c makes a 45° angle with wall 2. 19. c. First, convert the width (1 yard) into feet: 1 yard = 3 feet. Next, use A = lw = 6 × 3 = 18 square feet. (Note that all of the answer choices are in ft.2, so converting to feet is a good idea.) 20. a. The area of the square is A= s2 = 62 = 36 square cm. The area of the rectangle must then also be 36 square centimeters. Substituting this into the area formula, along with l = 9 you get: A = lw; 36 = 9 × w; w = 36 ÷ 9 = 4 centimeters. 21. d. You are told that Area = 9. If A = r2, then r2= 9, and r = 3. Circumference, C = 2r = 2 × 3 = 6 centimeters. Remember that perimeters and circumferences are measured

26.

27.

in units (like centimeters) and areas are measured in square units (like square centimeters). b. First, calculate the area in square feet. The area of a rectangle is lw, so A = lw = 860 feet × 560 feet = 481,600 square feet. Next, 1 acre use the conversion factor  43,56 0 ft.2 and multi1 acre 2 ply: 481,600 ft ×  43,56 0 ft. 2 ≈ 11.056 acres ≈ 11.06 acres. c. Area = lw. First, convert the mixed numbers to improper fractions: 127 inches = 97 inches 9 and 145 inches = 5 inches. Next, use these fractions in the formula: Area = lw = 97 × 95 = 81 11  square inches = 2 square inches. 35 35 b. The perimeter of a rectangle is the sum of all its sides: 160 + 160 + 80 + 80 = 480 feet. Next, convert to yards by multiplying 480 with the 1 yd. 1 yd.   conversion factor  3 ft. : 480 feet × 3 ft. = 160 yards. d. The curved markings indicate that the two bottom angles are equal. You can call these two equal angles y. Thus y + y + 40 = 180, 2y + 40 = 180; 2y = 140; y = 70. Angles x and y form a complete circle (360°). Thus, x = 360 – y° = 360° – 70° = 290°. c. The volume formula for a cube is V = s3, so here s3 = 8 and s = 2 in. The surface area of one face is s2 = 22 = 4 square inches. Since there are six faces, the total surface area is 6 × 4 square inches = 24 square inches. a. When the 2 × 2 squares are cut out, the length of the box is 3, and the width is 6. The height is 2: 3 2 6

The volume is 3 × 6 × 2, or 36. 28. d. Draw yourself a rectangle to represent the 12 feet × 15 feet floor. Since each tile is 6 inches by

139

–MEASUREMENT AND GEOMETRY–

6 inches, or 21 foot by 21 foot, you can see that you could get 24 tiles across the floor, and 30 tiles going down. Now you just multiply 24 by 30 to get the total tiles needed: 24 × 30 = 720. 29. d. Fill in the missing sides:

33.

2 2

34.

2 2

6

2 2 6

35.

Next, add up all the sides: P = 6 + 6 + 6(2) = 12 + 12 = 24 units. 30. d. Divide up the figure into squares as shown: 2 2

36.

2 2 2 2

The figure is composed of six squares. The area of each square is s2 = 22 = 4. Thus the total area is 6  4 = 24 square units. 31. b. Convert 26.2 miles to feet, and divide by the length of the walker’s stride to find how many steps this walker takes in a marathon: 1 mile = 5,280 feet, so 26.2 miles = 138,336 feet. Divide 138,336 by 1.96 feet per step to get 70,579.6. Round to the nearest whole number to get 70,580 steps. 32. c. The two lines through the sides of the triangle indicate that they are equal. The right angle is 90° and the two angles opposite the two equal sides will be equal. Since the interior angles of

140

37.

38.

a triangle add to 180°, the two equal angles must add to 180° – 90° = 90°. Thus each angle will be equal to 45°. Thus, angle C = 45°. a. Remember the formula for figuring out the area of a circle: A= r2. Circle A then is  32 or 9 and circle B is 52 or 25 , so the area of circle B is 16 greater than circle A. c. To find the area of the shaded region, subtract the area of the triangle from the area of the square. The area of the triangle is 21 bh = 21 (4)(4) = 8 square units, and the area of the square is s2 = 42 = 16 square units. Thus, the area of the shaded region is 16 – 8 = 8 square units. a. Set up an equation. (Remember, all the angles added up inside a four-sided figure equal 360°): 90 + 100 + x + 2x + 20 = 360, which is 3x + 210 = 360. Subtract 210 from both sides to get 3x = 150. Divide by 3 to get x = 50. c. For this question, you already know that the 3g weight is  cm3 . You need to find out how many cubic centimeters there are in the given cube, which is the volume of the cube. For a cube, the volume = side3. The given cube has a side = 5, so V = 53 = 5 × 5 × 5 = 125. Then, to find 3g the weight you multiply 125 cm3 ×  cm3 = 375 grams. c. Since BC = 24, BC will be half that, or 12. Thus, ABC is a right triangle with legs equaling 5 and 12. You can use the Pythagorean theorem to solve for the hypotenuse: a2 + b2 = c2 becomes 52 + 122 = c2, then 25 + 144 = c2, then 169 = c2, so c = 13. a. ABC is a 5-12-13 right triangle (see answer explanation for question 37) and ABC is double that, or 10-24-26. Thus, the perimeter of ABC is 5 + 12 + 13 = 30, and the perimeter of ABC is twice that, or 60. Thus, the difference is 60 – 30 = 30.

–MEASUREMENT AND GEOMETRY–

39. d. ABC is a 5-12-13 right triangle (see answer explanation for question 37) and ABC is double that, or 10-24-26. The base of ABC is 24, and its height is 10. Apply the area formula: A = 1 1 bh = (24)(10) = 120 units2. The base of 2 2 ABC is 12, and its height is 5. Apply the area formula: A = 21bh = 21 (12)(5) = 30 units2. Thus, the difference is 120 – 30 = 90 units. 40. a. You can use the Pythagorean theorem to solve for the missing leg: a2 + b2 = c2 becomes 12 + x2 = (10 )2, then 1 + x2 = 10, so x2 = 9, and x = 3. 41. d. The shaded area is the difference between the area of the square and the circle. Because the radius is 1, a side of the square is 2. The area of the square is s2 = 22 = 4, and the area of the circle is r2 = 12 = . Therefore, the answer is 4 – . 42. a. First, find the area of the circle: Area = r2, or 3.14 × 9, which equals 28.26 square inches. Then, notice there are 360° in a circle and 60 60 1 is one-sixth that ( 36 0 = 6). The shaded area is then only one-sixth the area of the total circle. Divide 28.26 by 6 to get 4.71 square inches. 43. d. After removing the circular bases, you are left with a flat rectangle. Since the height was 4.2 inches, the length of the rectangle is 4.2 inches. Since the circumference of the bases was C = 2r = 2 × 3.14 × 12 = 3.14 inches, the width of the rectangle is 3.14 inches Thus, the area of the new rectangular figure is lw = 4.2 × 3.14 = 13.188 inches square 44. d. The point lies on the circumference of a circle with a radius of 2.5 feet. Therefore, the distance that the point travels in one rotation is the length of the circumference of the circle, or 2r = 2(2.5) = 5 feet. Since the wheel spins at 2,640 revolutions per minute, the point travels 2,640 × 5 feet per minute = 13,200 feet per minute. Multiplying by 60 to find the distance traveled in one hour, you get 60 × 13,200 =

141

45.

46.

47.

48.

49.

50.

792,000 feet per hour. Dividing by 5,280 feet to convert to miles, you get 150 miles per hour. d. The curved length of the perimeter is one quarter of the circumference of a full circle: 14 2r, = 2 (272 )(3.5) = 7 × 272 = 22. The linear (straight) lengths are radii, so the solution is simply 22 + 2(3.5) or 29. d. Because the radius of the hemisphere is 3, and it is the same as half the base of the triangle, the base must be 6. Therefore, the area of the triangle is 12bh = 12 (4 × 6) = 12. The area of the circle, if it was a whole circle, is r2, which equals 9. Therefore, the area of a half-circle is 92. Adding gives 92 + 12. a. To get the height of the triangle (h), using the Pythagorean theorem: a2 + b2 = c2 becomes 62 + h2 = 102, then 36 + h2 = 100, and h2 = 64, so the height, h, equals 8. Then 5 is plugged in for the base and 8 for the height in the area equation A = 12bh. Thus, A = 12 (5)(8) = 20 square units. c. An algebraic equation can be used to solve this problem. The shortest side can be denoted s. Therefore, s + (s + 2) + (s + 4) = 24; 3s + 6 = 24, and s = 6. b. If the circle is 100 square inches, its radius must be 10 inches (because A = r2 and here A = 100).  A B is twice the radius, so it is 20 inches. d. The outer edge of the wheel is in contact with the ground. Since you are told to use 1 mile = 5,280 feet, you would be wise to convert the 12 inch radius to 1 foot. You can find the outer edge (circumference) by using C = 2r = 2(272 )(1) = 474 feet. Thus, each time it revolves it covers 474 feet. Divide 5,280 feet by 474 feet to find the number of revolutions in 1 mile: 5,280 ÷ 474 = 5,280 × 474 = 840 revolutions.

S E C T I O N

3

Vocabulary Prep for Civil Service Exams

A

ll civil service exams test vocabulary skills in some form. Nearly all include a section testing your ability to read and understand extended passages. Many also include questions about grammar, vocabulary, and spelling. There are good reasons for including these skills on civil service exams. To be an effective government employee, you must be able to read and comprehend memos, policy statements, procedural instructions, documents, and reports. Similarly, most positions require you to communicate effectively in writing. You can’t do that without some mastery of English vocabulary, grammar, and spelling. The good news is that these exams test basic skills. No one is going to ask you to read a complicated novel and interpret its symbolism. Nor will a civil service exam ask you to spell Australopithecus or to conjugate verbs in the future subjunctive tense (or even to know what the future subjunctive tense is, for that matter). All you need to do is to read a passage and answer some related questions, which will be pretty straightforward, and to recall some fundamental principles of grammar and spelling. The chapters that follow review the basic skills necessary to pass the vocabulary portion of your civil service exam. Remember, a rich vocabulary gives you a strong advantage in the workplace. When you have an extensive vocabulary, you can write clear descriptions; you can speak more fluently and with more confidence; you can understand more of what you read; and you can read more sophisticated texts. Achieving a good vocabulary does not come without hard work. Take the time now and make the commitment to improve your verbal skills for your civil service exam.

143

C H A P T E R

10

Vocabulary in Context

T

he vocabulary section of the civil service exam often includes a section of vocabulary in context questions. For this part of the exam, you will be asked to identify the meanings of vocabulary words used in sentences. Because you will not be able to use a dictionary during the exam, it is important to develop vocabulary strategies that will boost your score and give you the advantage you need. As you might expect, vocabulary in context questions ask you to determine the meanings of particular words. To prepare for this section of the exam, recall the skills you developed at an early age. First, it is a good idea to be an active reader. This is a skill you can practice every day. As you read the daily newspaper, your favorite magazine, or the latest book, have a dictionary handy. Look up as many unfamiliar words as you can so that your bank of vocabulary words becomes as large as possible. Second, be aware that you can use the context of a sentence to help you detect the meaning of a word. Simply put, this means that you can look for clues in and around the vocabulary word. For practice, try the following exercise to see how this can be done.

145

–VOCABULARY IN CONTEXT–

As a result of many meetings held by the Human Resources Department, a memo was written to help hiring supervisors present information about new procedures that benefit the company, the staff, and new employees during a new employee orientation seminar. The new procedures create a win-win situation for all concerned, and the Human Resources Department

wants to make sure that those people who are instrumental in making the program work have all the information they need. Imagine that your title is Hiring Supervisor, and you receive the following memorandum from the Human Resources Department. Read it carefully. Circle any words that are unfamiliar to you, but do not use a dictionary to look them up just yet.

TO: Hiring Supervisors FROM: Human Resources RE: New Employees In order for new employees to begin work in the office, the New Employee Introduction Manual has been compiled. This manual should be distributed to all new hires during an orientation seminar that you will conduct one week before a new employee begins work. During orientation, be sure to point out that not only does the information in the manual inform new employees about office protocol and employee benefits, but it gives them a sense of the new family they are about to join. As you leaf through the manual with new hires, note that the manual begins with basic office etiquette, procedures, and dress codes and then there is a segue to important information about pay schedules and benefits. Explain to your orientation group that with this manual in hand, new employees will have a more global view of the company. They will know what to expect and can ask questions that will make their new position a little more comfortable on the first day. The benefits of the orientation seminar, in addition to the manual, will make our workplace a more cohesive and productive environment for all employees.

As you read, you may have circled protocol or segue. By looking for context clues—the way the words are used in the paragraph—you can figure out what these words mean. What does protocol mean? Reread the sentence with the word protocol. “During orientation, be sure to point out that not only does the information in the manual inform new employees about office protocol and employee benefits, but it gives them a sense of the new family they are about to join.” Even if you have no idea what protocol means, you can still tell something about the word by how it

is used—by examining the words and ideas surrounding it. This is called determining word meaning through context. Like detectives looking for clues at a crime scene, you must look at the passage for clues that will uncover the definition of the word. Given the sentence you have here, you can begin to consider the definition of protocol. Since the manual informs new employees about office protocol and employee benefits, this tells you that protocol must be a procedure or system designed to make things run smoothly in the office. As you read the next sentence in the memo, you see that the sections of the manual cover many topics: etiquette, procedures, dress codes,

146

–VOCABULARY IN CONTEXT–

 Segue, in this case, can be defined as a. a disorganized flow of ideas. b. merely sketchy details and descriptions. c. uninterrupted movement from one stage to the next. d. wordy and verbose language.

salaries, and employee benefits. At this point, you should be able to take a pretty good guess at the definition of the word protocol.  The best definition of the word protocol is a. a meeting’s agenda. b. a code of correct procedure. c. a salary schedule. It cannot be choice a because nowhere in the passage does it state that protocol is a list of items covered in a meeting. While a salary schedule, choice c, is determined by a certain procedure, it is only part of the scope of an office system. The correct answer is choice b, a code of correct procedure. What does segue mean? Look again at the sentence in which segue is used. “As you leaf through the manual with new hires, note that the manual begins with basic office etiquette, procedures, and dress codes and then there is a segue to important information about pay schedules and benefits.” Again, even if you have no idea what segue means, you can still tell what kind of word it is by the way it is used in the sentence.  Because the word segue falls between a list of basic office etiquette, procedures, and dress codes and important information about pay schedules and benefits, you know this word is a. an interference in the sentence. b. a transition in the sentence.

The correct answer is choice c, uninterrupted movement from one state to the next. It cannot be choice b or d because there is no indication that anything in the manual is omitted or for that matter, wordy or verbose. Choice a is not a suitable answer because the manual, as it is outlined, appears to be well ordered.



How Much Context Do You Need?

In the previous example, you would still be able to understand the main message of the memorandum even if you did not know—or could not figure out— the meanings of protocol and segue. In some cases, though, your understanding of a sentence depends on your understanding of a particular word or phrase. For example, can you understand the following sentence without knowing what adversely means? The new policy will adversely affect all employees.

There is one very obvious clue. As the hiring supervisor leafs through the manual, he or she pages through all sections of the text, highlighting the basic elements contained in the opening chapters and then notes that the chapters switch or move to important facts about salaries and benefits.

You might not understand it in this short sentence, and if you are an employee, you certainly would want to know how you are going to be affected. More defining clues for the word adversely will help you know whether it is something good or bad:

147

The new policy will adversely affect all employees; it will freeze their pay, limit their vacation time, and reduce their health benefits.

–VOCABULARY IN CONTEXT–



 In the sentence, adversely most nearly means a. mildly or slightly. b. regularly or steadily. c. negatively or unfavorably. d. immediately or swiftly. The correct answer is choice c, negatively or unfavorably. The addition of the second part of the sentence now tells you exactly how the new policy will affect the employees: “It will freeze their pay, limit their vacations, and reduce their benefits.” It is not choice a, a slight or mild change, nor is it choice b, a regular or steady change. You do not know if it is an immediate or swift change, choice d, because the sentence says nothing about the time frame in which this change will take place. Remember, good detectives do not make assumptions they are not able to support with facts, and there are no facts in this sentence to support the assumption that the changes will take place immediately. Thus, choice c is the best answer. You may also have noticed that adversely is very similar to the word adversary. If you know that an adversary is a hostile opponent or enemy, then you know that adversely is not likely to be something positive. Or, if you know the word adversity—hardship or misfortune— then you know that adversely must mean something negative or difficult. All of these words share the same root: advers-. The only change is in the endings. Being able to determine the meaning of unfamiliar words from their context is an essential vocabulary skill. Sometimes you will encounter an unfamiliar word whose meaning is indecipherable without a dictionary. More often than not, though, a careful look at the context will give you enough clues to interpret the definition.

Practice Questions

Read the following paragraph. Some words that may be unfamiliar to you are in italics. After you have read and understood the paragraph, explain the context clues that helped you with the meaning of the italicized words. Write your answer on the lines provided on the next page.

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Medical researchers can now verify that college freshman living in dormitories are at a greater risk of contracting meningitis than other college students. Meningococcal meningitis is a tenacious bacterial infection of the membranes around the brain and spinal chord that, if left untreated, can be fatal. Symptoms include fever, neck stiffness, and constant pain from a chronic headache. College officials are using this information as an inducement for vaccinating incoming freshman. Many universities are now offering this vaccine either free or for a nominal fee. The vaccination’s protracted effectiveness is three to five years.

–VOCABULARY IN CONTEXT–



Answers

After reading the paragraph, you learn that a study has been done that shows that college freshman living in dorms have a higher risk of getting meningitis; therefore, you can conclude that verify means confirm. Because this disease can be fatal, you can understand that once contracted, it is not easily wiped out; thus, you can infer that tenacious means persistent and not easily stopped. Because the symptoms include constant pain

from a chronic headache, you can deduce that chronic means continual. It makes sense that college officials are concerned about the possible outbreak of such a disease on campus and would take measures to prevent its occurrence, so you can infer that inducement means encouragement. Students would be encouraged to take the vaccine if it were free or inexpensive; therefore, you can see that nominal means a small amount. Finally, you can gather that protracted means drawn out by the mention that the vaccine will last from three to five years.

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C H A P T E R

11

Synonyms and Antonyms

O

n the civil service exam, your grasp of the English language will be measured with many different types of vocabulary questions. Frequently, synonym and antonym questions are used to assess your vocabulary aptitude. This chapter covers both of these types of questions. In addition, it provides useful tips and practice questions that will help you increase your chance of success on this part of the exam. A common measure of verbal skills on standardized tests like the civil service exam is the ability to recognize synonyms and antonyms. Synonyms are words that share the same meaning or nearly the same meaning as other words. Antonyms are words with opposite meanings. Many antonyms seem obvious (good and bad, night and day, noisy and silent), but others are not as easily recognizable. This is because many words have more than one meaning. For example, the word clear could mean cloudless or transparent or unmistakable. And for each of those meanings, clear has an opposite. If an antonym isn’t obvious, think about other possible meanings of the word.

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Test questions often ask you to find the synonym or antonym of a word. If you are lucky, the word will be surrounded by a sentence that helps you guess what the word means (this is vocabulary in context—see Chapter 10), but the test question could list just a synonym or antonym and four answer choices. In this case, you have to figure out what the word means without any help from context clues. Questions that ask for synonyms and antonyms can be difficult because they require you to have a relatively large vocabulary. Not only do you need to know the word in question, but you may be faced with four choices that are unfamiliar to you, too. Usually the best strategy is to look at the structure of the word. See if a part of the word—the root—looks familiar. Often you will be able to determine the meaning of a word within the root. (See “Appendix 5” on page 289 for a list of common word roots.) For instance, the root of credible is cred, which means to trust or believe. Knowing this, you will be able to understand the meaning of incredible, sacred, and credit. Looking for related words that have the same root as the word in question can help you choose the correct answer—even if it is by process of elimination. Another way to dissect meaning is to look for prefixes and suffixes. Prefixes come before the word root, and suffixes are found at the end of a word. Either of these elements can carry meaning or change the use of a word in a sentence. For instance, the prefix can change the meaning of a root word to its opposite: necessary, unnecessary. A suffix like less can change the meaning of a noun: pain to painless. To identify most word parts—word root, prefix, or suffix—the best strategy is to think of words you already know that carry the same root, suffix, or prefix. Let what you know about those words help you find the meaning of words that are less familiar.



Denotation and Connotation

The denotation of a word is its dictionary definition. For instance, look at the dictionary definitions for the following words. procrastination: to postpone or delay needlessly lazy: to be resistant to work or exertion; slow-moving or sluggish inactive: not active or tending to be active; not functioning or operating The connotation of a word is its tone. In other words, it is the feeling or emotion you get when you hear a word. Sometimes, the connotation can be favorable or positive. Other times the connotation can be unfavorable or negative. Then again, some words do not arouse any emotion at all and have a neutral connotation. Look again at the three words just listed. Their connotations are listed here with an explanation for a favorable, unfavorable, or neutral designation.

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procrastination—favorable. You have often heard people say that they succumbed to procrastination, and that admission is received sympathetically and somewhat approvingly by others because everyone has procrastinated at one time or another. To admit to this trait is considered acceptable at times. lazy—unfavorable. Laziness, which is similar in definition to procrastination, is most assuredly unflattering. The connotation or tone of this word brings up feelings that are definitely unappealing. inactive—neutral. This word does not elicit any favorable or unfavorable emotions. It is considered a neutral word in this group of three, yet its meaning is similar to the others.

–SYNONYMS AND ANTONYMS –



Clarity

Mark Twain said, “The difference between lightning and the lightning bug is the difference between the right word and the almost right word.” Taking this comment into consideration, it is important to know that there are often many synonyms for one word. It is essential to be as clear as possible when choosing synonyms. While some synonyms can be similar, they are rarely identical. For instance, the words bountiful, ample, plentiful, and glut suggest abundance. However, one of these words suggests an overabundance. While you can have a bountiful, ample, or plentiful supply of food on the table for Thanksgiving dinner, a glut of food is an excessive amount of food that suggests there will be waste involved. It is important to choose your words carefully.



3. Which word means the same as ecstatic? a. inconsistent b. positive c. wild d. thrilled 4. Which word means the same as affect? a. accomplish b. cause c. sicken d. influence 5. Which word means the same as continuous? a. intermittent b. adjacent c. uninterrupted d. contiguous 6. Which word means the same as courtesy? a. civility b. congruity c. conviviality d. rudeness

Practice Questions

For questions 1–15, choose the synonym. 1. Which word means the same as enthusiastic? a. adamant b. available c. cheerful d. eager

7. Which word means the same as frail? a. vivid b. delicate c. robust d. adaptable

2. Which word means the same as adequate? a. sufficient b. mediocre c. proficient d. average

8. Which word means the same as recuperate? a. mend b. endorse c. persist d. worsen

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9. Which word means the same as meager? a. majestic b. scarce c. tranquil d. adequate 10. Which word means the same as composure? a. agitation b. poise c. liveliness d. stimulation 11. Which word means the same as eccentric? a. normal b. frugal c. peculiar d. selective 12. Which word means the same as commendable? a. admirable b. accountable c. irresponsible d. noticeable 13. Which word means the same as passive? a. inactive b. emotional c. lively d. woeful 14. Which word means the same as vast? a. attentive b. immense c. steady d. slight

15. Which word means the same as comply? a. subdue b. entertain c. flatter d. obey For questions 16–25, choose the word that has the same or nearly the same meaning as the capitalized word. 16. JOURNAL a. trip b. receipt c. diary d. list 17. OPPORTUNITY a. sensitivity b. arrogance c. chance d. reference 18. INVENT a. insert b. discover c. apply d. allow 19. SPHERE a. air b. spread c. globe d. enclosure 20. REFINE a. condone b. provide c. change d. purify

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21. PLEDGE a. picture b. idea c. quote d. promise

27. What word is the opposite of delay? a. slow b. hasten c. pause d. desist

22. GANGLY a. illegally b. closely c. ugly d. lanky

28. What word is the opposite of soothe? a. increase b. comfort c. aggravate d. delight

23. SAGE a. wise b. obnoxious c. conceited d. heartless

29. Which word means the opposite of moderate? a. original b. average c. final d. excessive

24. NAVIGATE a. search b. decide c. steer d. assist

30. Which word means the opposite of reveal? a. disclose b. achieve c. retreat d. conceal

25. DORMANT a. hidden b. slumbering c. rigid d. misplaced

31. Which word means the opposite of initial? a. first b. crisis c. final d. right

For questions 26–40, choose the antonym.

32. Which word means the opposite of brittle? a. flexible b. breakable c. grating d. thin

26. Which word means the opposite of prompt? a. punctual b. slack c. tardy d. regular

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33. Which word means the opposite of capable? a. unskilled b. absurd c. apt d. able

39. Which word means the opposite of forsake? a. admit b. abandon c. submit d. cherish

34. What word is the opposite of stray? a. remain b. inhabit c. wander d. incline

40. What word is the opposite of restrain? a. control b. liberate c. maintain d. distract

35. What word is the opposite of dainty? a. delicate b. coarse c. harsh d. delicious

For questions 41–50, choose the word that has the opposite meaning as the capitalized word.

36. Which word means the opposite of craving? a. desire b. nonchalance c. motive d. repugnance 37. Which word means the opposite of ferocious? a. docile b. savage c. explosive d. noble 38. Which word means the opposite of grueling? a. effortless b. casual c. exhausting d. empty

41. ABSORB a. acquire b. repel c. consume d. assist 42. CRITICAL a. inimical b. judgmental c. massive d. trivial 43. NIMBLE a. sturdy b. sluggish c. thoughtless d. relaxed 44. TRANQUIL a. agitated b. explicit c. assertive d. composed

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45. SPRIGHTLY a. eager b. lofty c. dull d. local

48. AMIABLE a. dangerous b. permissive c. aloof d. congenial

46. INFANTILE a. despicable b. adolescent c. mature d. perpetual

49. COMPETENT a. incomplete b. intense c. inept d. massive

47. IMPULSIVE a. secure b. mandatory c. rash d. cautious

50. PROMOTE a. explicate b. curtail c. concede d. remote

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Answers 24. c. To navigate and to steer both mean to direct a course. 25. b. Dormant and slumbering both mean sleeping. 26. c. Prompt means punctual; tardy means late. 27. b. To delay is to slow; to hasten is to hurry. 28. c. To soothe is to comfort; to aggravate is to irritate. 29. d. Moderate means average; excessive means extreme. 30. d. To reveal is to disclose; to conceal is to hide. 31. c. Initial means first; final means last. 32. a. Brittle means breakable; flexible means pliable. 33. a. Capable means able; unskilled means unable. 34. a. To stray is to wander; to remain is to stay. 35. b. Dainty means delicate; coarse means indelicate. 36. d. Craving means desire; repugnance means aversion. 37. a. Ferocious means savage; docile means tame. 38. a. Grueling means exhausting; effortless means easy. 39. d. To forsake is to abandon; to cherish is to nurture. 40. b. To restrain is to control; to liberate is to release. 41. b. Absorb means to take in or consume; to repel is to reject or force away. 42. d. To be critical is to be important or vital to something; to be trivial is to be unimportant. 43. b. Nimble means quick and light in motion; sluggish means slow or inactive. 44. a. Tranquil means peaceful; agitated means disturbed or excited.

1. d. Enthusiastic means eager or excited. 2. a. If something is adequate, it is sufficient. 3. d. A person who is ecstatic is thrilled or exhilarated. 4. d. To affect means to influence. 5. c. Continuous means marked by uninterrupted extension in space and time. 6. a. A courtesy implies being courteous or mannerly; it is civility. 7. b. A frail person is weak and delicate. 8. a. Recuperate means to heal; to mend. 9. b. Meager and scarce both mean lacking. 10. b. If you gain your composure, you have poise. 11. c. An eccentric person is considered to be peculiar. 12. a. Commendable is the same as admirable. 13. a. Passive means not active. 14. b. Vast means very great in size; immense. 15. d. To comply is the same as to obey. 16. c. A journal and a diary are both records of daily happenings. 17. c. An opportunity to do something is the same as a chance to do it. 18. b. Invent means to create or to discover. 19. c. Sphere and globe both mean ball or orb. 20. d. To refine and to purify both mean to remove impurities. 21. d. Pledge and promise both mean a declaration that one will do something. 22. d. Gangly and lanky both mean tall, thin, and awkward. 23. a. Sage and wise both mean intelligent or perceptive.

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45. c. Sprightly means lively; dull suggests a lack or loss of keenness or zest. 46. c. Infantile means childish, mature means grown up. 47. d. To be impulsive is to be swayed by emotion or to make rash decisions; to be cautious is to show forethought.

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48. c. Amiable means friendly; the opposite of friendly is aloof. 49. c. Competent means having adequate abilities; inept means incapable or not competent. 50. b. To promote is to advance someone to a higher rank or to advocate something; to curtail is to cut something short.

C H A P T E R

12

Reading Comprehension

B

ecause understanding what you read is such a vital skill, most civil service exams include a reading comprehension section that tests your ability to understand what you read. To read effectively, you should be able to find the main idea of a passage, select the topic sentence, locate basic support material or details, discern fact from opinion, and make inferences. This chapter reviews each of these skills. The reading comprehension portion of the civil service exam is usually presented as a multiple choice test and will ask questions based on brief passages. Reading comprehension questions offer you two advantages as a test taker. First, you do not need any prior knowledge about the topic of the passage. Second, you will be tested only on the information presented in the passage. The disadvantage is that you have to know where and how to find the information you need under certain time constraints and in an unfamiliar text. This somewhat stressful combination makes it easy to choose one of the wrong answer choices, especially since the choices are deliberately designed to mislead you. If you are in a hurry, it is easy to make a mistake.

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As you study this reading comprehension section, understand that your vocabulary skills play a vital role when you have to decipher any written text. Sometimes, just one difficult word can skew your understanding of a sentence. Two or three unknown words can make a passage difficult, or even impossible, to interpret. The study of vocabulary in combination with reading comprehension go hand in hand as you continue your test preparation. The best way to do well on a reading comprehension test is to be very familiar with the kinds of questions that are typically asked, and then to know how to respond to these questions. Questions most frequently ask you to: ■ ■ ■ ■ ■ ■

determine the main idea of the passage. identify a specific fact or detail in the passage. identify the topic sentence. discern fact from opinion. make an inference based on the passage. define a vocabulary word from the passage. (Refer to Chapter 10 to practice this skill.)

Once you know the kinds of questions that will be asked, you can develop some strategies to help you choose correct answers. To do this, you must be a discriminating reader and know where to look for the information, facts, and details you need to help you choose correctly. One strategy used by many readers is highlighting and underlining. By highlighting or underlining key words and phrases, you can make important details stand out. This helps you quickly find the information later when you need to answer a question or write a summary. To highlight key words and ideas, you must be able to determine which facts and ideas are most important.

Here are three guidelines for highlighting or underlining your text. 1. Be selective. If you highlight four sentences in a five-sentence paragraph, this will not help you. The key is to identify what is most important in the paragraph. Ask yourself two questions: ■ What is the main point the author is trying to make—what is the main idea of the paragraph? ■ What information is emphasized or seems to stand out as especially important? 2. Watch for word clues. Certain words and phrases indicate that key information will follow. Words and phrases such as most important, the key is, and significantly are clues to watch out for. 3. Watch for visual clues. Key words and ideas are often boldfaced, underlined, or italicized. They may be boxed or repeated in a sidebar as well. For practice, read the following paragraph and answer the questions that follow. The answer explanation following each type of question—main idea, detail/support material, topic sentence, fact/opinion, and inference—will point out reading comprehension strategies that help you choose the correct answer. Today’s postal service is more efficient and reliable than ever before. Mail that used to take months to move by horse and by foot now moves around the country in days or hours by truck, train, and plane. First class mail usually moves from New York City to Los Angeles in three days or fewer. If your letter or package is urgent, the U.S. Postal Service offers Priority Mail and Express Mail services. Priority Mail offers delivery to most locations in the United States in two to three days or fewer. Express Mail is guaranteed to get your package there overnight. Additionally, the U.S. Postal Service offers lower rates for the same services offered by many competitors.

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Main Idea Question

Fact/Detail Question

1. What is the main idea of this paragraph? a. The U.S. Postal Service offers many services. b. Express Mail is a good way to send urgent mail. c. First class mail usually takes three days or fewer. d. Mail service today is more effective and dependable. If you selected choice a, you would be choosing the subject of the paragraph, not the main idea. The main idea must say something about the subject. To accurately find the main idea of a text, remember that it is usually an assertion about the subject. An assertion is a statement that requires evidence or proof to be accepted as true. While the main idea of a passage is an assertion about its subject, it is something more. It is the idea that holds together or controls the passage. The other sentences and ideas in the passage will all relate to that main idea and serve as evidence that the assertion is true. You might think of the main idea as an umbrella that is held over the other sentences. It must be general enough or big enough to cover all of these ideas underneath it (in the paragraph or passage). Choice b is too specific to be the main idea; it tells you only about Express Mail. It does not include any information about Priority Mail or first class mail, so it cannot be the main idea of the paragraph. Choice c is also too specific. It tells you about first class mail only, so this choice can be excluded. Choice d is general enough to encompass the entire passage. The rest of the sentences in the paragraph support the idea that this sentence asserts. Each sentence offers proof that the postal expresses the writer’s purpose—to show the efficiency and reliability of today’s postal service.

2. Today’s mail is transported by a. foot. b. horse. c. trucks, trains, and planes. d. overnight services. Choices a and b are mentioned in the paragraph, and you may mistakenly choose one of these if you only scan the paragraph quickly. However, if you read more closely, you will see that in the past, “Mail used to take months to move by horse and by foot,” but it “now moves around the country in days or hours by truck, train, and plane,” choice c. Choice d is misleading. Overnight mail services are transported by truck, train, and plane as well.

Topic Sentence Question 3. Of the following sentences, which one is the topic sentence? a. Mail that used to take months to move by horse and by foot now moves around the country in days or hours by truck, train, and plane. b. Today’s postal service is more efficient and reliable than ever before. c. If your letter or package is urgent, the U.S. Postal Service offers Priority Mail and Express Mail services. d. Express Mail is guaranteed to get your package there overnight. You will notice that in the paragraph, the main idea is expressed clearly in the first sentence, choice b. A sentence such as this one that clearly expresses the main idea of a paragraph or passage is called the topic sentence. In many cases, you will find the topic

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sentence at the beginning of the paragraph, but this is not a hard and fast rule. The topic sentence can be found in the middle or at the end of a paragraph. However, for the sentence to be labeled a topic sentence, it must be an assertion, and it needs proof. The proof is found in the facts and ideas that make up the rest of the paragraph. Choices a, c, and d are sentences that offer specific facts and ideas that support choice b.

Inference Question 4. Based on the information in the paragraph, it is safe to say that a. it is economical for businesses to take advantage of Express Mail services. b. the old-fashioned pony express system of mail delivery did not work. c. first class mail service is unreliable. d. there is no way to deliver urgent mail.

Fact/Opinion Question 3. “Express Mail is guaranteed to get your package there overnight.” This statement is a(n) a. fact. b. opinion. Facts are things known for certain to have happened, to be true, or to exist. Opinions are things believed to have happened, believed to be true, or believed to exist. As you can see, the key difference between fact and opinion lies in the difference between believing and knowing. Opinions may be based on facts, but they are still what you think, not what you know. Opinions are debatable; facts are not. The statement in the question, “Express Mail is guaranteed to get your package there overnight,” is a fact, so choice a is correct.

An inference is a conclusion that can be drawn based on fact or evidence. You can infer that businesses could take advantage of Express Mail service to speed up deliveries, choice a, based on the evidence in the paragraph. “Express Mail is guaranteed to get your package there overnight,” justifiably supports this inference. Choices b, c, and d cannot be inferred based on any concrete evidence from the paragraph. Knowing that reading comprehension questions can include main idea, topic sentence, detail, fact/opinion, or inference questions is a practical beginning for reading comprehension skills.

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Practice Questions

Read the following paragraphs and answer the reading comprehension questions based on your knowledge of the main idea of each paragraph. If you are a fitness walker, there is no need for a commute to a health club. Your neighborhood can be your health club. You do not need a lot of fancy equipment to get a good workout, either. All you need is a well-designed pair of athletic shoes. 1. This paragraph best supports the statement that a. fitness walking is a better form of exercise than weight lifting. b. a membership in a health club is a poor investment. c. walking outdoors provides a better workout than walking indoors. d. fitness walking is a convenient and valuable form of exercise.

One New York publisher has estimated that 50,000 to 60,000 people in the United States want an anthology that includes the complete works of William Shakespeare. What accounts for this renewed interest in Shakespeare? As scholars point out, his psychological insights into both male and female characters are amazing, even today. 3. This paragraph best supports the statement that a. Shakespeare’s characters are more interesting than fictional characters today. b. people today are interested in Shakespeare’s work because of the characters. c. academic scholars are putting together an anthology of Shakespeare’s work. d. New Yorkers have a renewed interest in the work of Shakespeare. There are no effective boundaries when it comes to pollutants. Studies have shown that toxic insecticides—already banned in many countries— are riding the wind from countries where they remain legal. Compounds such as DDT and toxaphene have been found in remote places like the Yukon and other Arctic regions.

Critical reading is a demanding process. To read critically, you must slow down your reading and, with pencil in hand, perform specific operations on the text. Mark up the text with your reactions, conclusions, and questions. In other words, when you read, become an active participant.

4. This paragraph best supports the statement that a. bans on toxins have done little to stop the spread of pollutants. b. more pollutants find their way into polar climates than they do into warmer areas. c. studies show that many countries have ignored their own anti-pollution laws. d. DDT and toxaphene are the two most toxic insecticides in the world.

2. This paragraph best supports the statement that a. critical reading is a slow, dull, but essential process. b. the best critical reading happens at critical times in a person’s life. c. readers should get in the habit of questioning the truth of what they read. d. critical reading requires thoughtful and careful attention.

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7. This paragraph best supports the statement that a. stone tools were not really technology. b. stone tools were in use for two and a half million years. c. there is no way to know when stone tools first came into use. d. in today’s world, new technologies are constantly being developed.

The Fourth Amendment to the Constitution protects citizens against unreasonable searches and seizures. No search of a person’s home or personal effects may be conducted without a written search warrant issued on probable cause. This means that a neutral judge must approve the factual basis justifying a search before it can be conducted. 5. This paragraph best supports the statement that police officers cannot search a person’s home or private papers unless they have a. legal authorization. b. direct evidence of a crime. c. read the person his or her constitutional rights. d. a reasonable belief that a crime has occurred.

Read the following paragraphs and choose the correct fact or detail to answer the questions. Ratatouille is a dish that has grown in popularity over the last few years. It features eggplant, zucchini, tomato, peppers, and garlic chopped, mixed, sautéed, and finally, cooked slowly over low heat. As the vegetables cook slowly, they make their own broth, which can be extended with a little tomato paste. The name ratatouille comes from the French word touiller, meaning to mix or stir together.

Mathematics allows us to expand our consciousness. Mathematics tells us about economic trends, patterns of disease, and the growth of populations. Math is good at exposing the truth, but it can also perpetuate misunderstandings and untruths. Figures have the power to mislead people.

8. Which of the following is the correct order of steps for making ratatouille? a. Chop vegetables, add tomato paste, stir or mix together. b. Mix the vegetables together, sauté them, and add tomato paste. c. Cook the vegetables slowly, mix them together, add tomato paste. d. Add tomato paste to extend the broth and cook slowly over low heat.

6. This paragraph best supports the statement that a. the study of mathematics is dangerous. b. the study of mathematics can be both beneficial and confusing. c. the study of mathematics is more important than other disciplines. d. the power of numbers is that they cannot lie. Human technology began with the development of the first stone tools about two and a half million years ago. In the beginning, the rate of development was slow, and hundreds of thousands of years passed without many technological changes. Today, new technologies are reported daily on television and in newspapers.

9. Ratatouille can best be described as a a. French pastry. b. sauce to put over vegetables. c. pasta dish extended with tomato paste. d. vegetable stew.

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12. According to the passage, each household a. may use only one recycling container. b. must use the new recycling container. c. should use the new recycling container. d. must buy a new recycling container.

After a snow or ice fall, the city streets are treated with ordinary rock salt. In some areas, the salt is combined with calcium chloride, which is more effective in below-zero temperatures and which melts ice better. This combination of salt and calcium chloride is also less damaging to foliage along the roadways. 10. In deciding whether to use ordinary rock salt or the salt and calcium chloride mixture on a particular street, which of the following is NOT a consideration? a. the temperature at the time of treatment b. the plants and trees along the street c. whether there is ice on the street d. whether the street is a main or secondary road

13. According to the passage, which of the following is true about the new containers? a. The new containers are far better than other containers in every way. b. The new containers will help increase the efficiency of the recycling program. c. The new containers hold more than the old containers did. d. The new containers are less expensive than the old.

11. According to the snow treatment passage, which of the following is true? a. If the temperature is below zero, a salt and calcium chloride mixture is effective in treating snow- and ice-covered streets. b. Crews must wait until the snow or ice stops falling before salting streets. c. Major roads are always salted first. d. If the snowfall is light, the city road crews will not salt the streets because this would be a waste of the salt supply.

Read the following paragraphs and choose the topic sentence that best fits the paragraph.

Many cities have distributed standardized recycling containers to all households. One city attached the following directions: “We prefer that you use this new container as your primary recycling container, as this will expedite pick-up of recyclables. Additional recycling containers may be purchased as needed from the Sanitation Department.”

14. a. The taste and aroma of spices are the main elements that make food such a source or fascination and pleasure. b. The term might equally bring to mind Indian curry made thousands of miles away or those delicious barbecued ribs sold down at Harry’s. c. It is exciting to find a good cookbook and experiment with spices from other lands— indeed, it is one way to travel around the globe.

Spices is a pleasant word, whether it connotes fine French cuisine or down-home cinnamon-flavored apple pie. . In the past, individuals traveled the world seeking exotic spices for profit and, in searching, have changed the course of history. Indeed, to gain control of lands harboring new spices, nations have actually gone to war.

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d. The history of spices, however, is another matter altogether, and it can be filled with danger and intrigue. It weighs less than three pounds and is hardly more interesting to look at than an overly ripe cauliflower. . It has created poetry and music, planned and executed wars, devised intricate scientific theories. It thinks and dreams, plots and schemes, and easily holds more information than all the libraries on Earth. 15. a. The human brain is made of gelatinous matter and contains no nerve endings. b. The science of neurology has found a way to map the most important areas of the human brain. c. Nevertheless, the human brain is the most mysterious and complex object on earth. d. However, scientists say that each person uses only 10% of brainpower over the course of a lifetime. Gary is a very distinguished-looking man with a touch of gray at the temples. Even in his early fifties, he is still the one to turn heads. He enjoys spending most of his time admiring his profile in the mirror. In fact, he considers his good looks to be his second most important asset in the world. The first, however, is money. He was fortunate enough to be born into a wealthy family, and he loves the power his wealth has given him. . He can buy whatever he desires. Gary checks the mirror often and feels great delight with what he sees.

16. a. Gary’s gray hair is his worst characteristic. b. Conceit is the beginning and the end of Gary’s character: conceit of person and situation. c. Gary feels blessed to be wealthy and the joy consumes his every thought. d. The only objects of Gary’s respect are others who hold positions in society above him. Read the following topic sentences and choose the sentence that best develops or supports the topic sentence. 17. Life on Earth is ancient, and at its first appearance, unimaginably complex. a. Scientists place its beginnings at some three billion years ago, when the first molecule floated up out of the ooze with the unique ability to replicate itself. b. The most complex life form is, of course, the mammal—and the most complex mammal is humankind. c. It is unknown exactly where life started— where the first molecule was “born” that had the ability to replicate itself. d. Darwin’s theory of evolution was one attempt to explain what essentially remains a great mystery. 18. The continuing fascination of the public with movie star Marilyn Monroe is puzzling, yet it is still strong, even after many decades. a. She became a star in the 1950s and died in 1962. b. The film that most clearly demonstrates her talent is The Misfits. c. Her name was originally Norma Jean, but she changed it to Marilyn. d. One reason might simply be her life’s sad and premature end.

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19. One scientific theory of the origin of the universe is the much misunderstood big bang theory. a. Physicists now believe they can construct what happened in the universe during the first three minutes of its beginning. b. Many scientists believe that, during microwave experiments, you can actually “hear” echoes of the big bang. c. The popular notion is that the big bang was a huge explosion in space, but this is far too simple a description. d. The big bang theory, if accepted, convinces us that the universe was not always as it is now.

21. The reintroduced wolves are producing more offspring than expected. a. Ranchers and some biologists are protesting the reintroduction of the wolves. b. The gray wolf will be taken off the list of endangered species in the northern Rocky Mountains when ten breeding pairs reside in a region for three years. c. There are active efforts to reintroduce wolves to national parks in the United States. d. The success of an attempt to reintroduce red wolves to parts of North Carolina is not yet clear.

20. There is no instruction by the old bird in the movements of flight, no conscious imitation by the young. a. The most obvious way in which birds differ from humans in behavior is that they can do all that they have to do, without ever being taught. b. More extraordinary than a bird being able to fly untaught is that it is able to build a nest untaught. c. Young birds frequently make their first flights with their parents out of sight. d. Young birds brought up by hand in artificial nests will build the proper kind of nest for their species when the time comes.

22. The Puritans established a wide variety of punishments to enforce their strict laws. a. The Puritans believed that some lawbreakers should be shamed in public by the use of stocks and the pillory. b. Disobedient children would feel the sting of the whip. c. The Eighth Amendment of the Bill of Rights prohibits cruel and unusual punishment. d. Today, many of the punishments used by the Puritans in Massachusetts Bay seem cruel and excessive.

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Read the following supporting sentences and choose the sentence that would make the best topic sentence. 23. Irish Catholics continued to fight against British rule. a. The struggle today is over the control of these six counties. b. For centuries, all of Ireland was ruled by Great Britain. c. Six counties in the north—where Protestants outnumber Catholics two to one—remained a part of Great Britain and became known as Northern Ireland. d. Political violence has claimed many lives in Northern Ireland. 24. In Oklahoma, a girl is forbidden to take a bite from her date’s hamburger. a. It is illegal for teenagers to take a bath during the winter in Clinton, Indiana. b. On Sunday, children may not spin yo-yos in Memphis, Tennessee. c. It may be hard to believe, but these strange laws are still on the books! d. It is illegal to parade an elephant down Main Street in Austin, Texas. 25. The hairs themselves are very sensitive. a. A cat’s whiskers are among the most perfect organs of touch. b. The roots are provided with highly sensitive nerve endings. c. Serving as feelers, they aid the cat’s ability to move in the dark. d. This is most important for a cat that does its prowling at night.

26. French explorers probably taught the Inuit Eskimos how to play dominoes. a. It was known in 181 A.D. in China. b. Also, it was played during the 1700s in Italy. c. The game of dominoes has been popular for centuries. d. From Italy, it was introduced to the rest of the world. 27. It is a fact that people are now living longer than ever before for many reasons. a. Some people in Russia’s Caucasus Mountains live to be over one hundred years of age. b. No one seems to understand this phenomenon. c. Advances in medical science have done wonders for longevity. d. The people in this region do not seem to gain anything from medical science. 28. For 16 years, he spread violence and death throughout the west. a. Jesse was gunned down on April 3, 1882. b. He left a trail of train and bank robberies. c. His crimes were committed during the late 1860s. d. Jesse Woodson James was the most legendary of all American outlaws.

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Read the following questions that ask you to differentiate fact from opinion. Write F in the blank if the statement is a fact and O if it is an opinion. 29.

Mr. Orenstein is a terrific boss.

30.

Many companies have dress-down days on Fridays.

31.

The use of computer equipment and software to create high quality printing for newsletters, business cards, letterhead, and brochures is called Desktop Publishing, or DTP. The most important part of any DTP project is planning. Before you begin, you should know your intended audience, the message you want to communicate, and what form your message will take.

Dress-down days improve employee morale.

32.

Wednesday is the fourth day of the week.

33.

Wednesday is the longest day of the week.

34.

35.

39. This paragraph best supports the statement that a. DTP is one way to become acquainted with a new business audience. b. computer software is continually being refined to produce more high quality printing. c. the first stage of any proposed DTP project should be organization and design. d. the planning stage of any DTP project should not include talking with the intended audience.

There are many different ways to invest your money to provide for a financially secure future. Many people invest in stocks and bonds.

36.

Savings accounts and CDs (certificates of deposit) are the best way to invest your hardearned money.

37.

Stocks and bonds are often risky investments.

38.

Savings accounts and CDs are fully insured and provide steady, secure interest on your money.

Read the following paragraphs and respond to the questions.

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–READING COMPREHENSION –

d. do not mark the containers they pick up with a warning that those containers contain sharp objects.

Many office professionals have expressed an interest in replacing the currently used keyboard, known as the QWERTY keyboard, with a keyboard that can keep up with technological changes and make offices more efficient. The best choice is the Dvorak keyboard. Studies have shown that people using the Dvorak keyboard can type 20–30% faster and are able to cut their error rate in half. Dvorak puts vowels and other frequently used letters right under the fingers—on the home row—where typists make 70% of their keystrokes. 40. This paragraph best supports the statement that the Dvorak keyboard a. is more efficient than the QWERTY. b. has more keys right under the typists’ fingers than the QWERTY. c. is favored by more typists than the QWERTY. d. is—on average—70% faster than the QWERTY. Every year, Americans use over one billion sharp objects to administer health care in their homes. These sharp objects include lancets, needles, and syringes. If not disposed of in puncture-resistant containers, they can injure sanitation workers. Sharp objects should be disposed of in hard plastic or metal containers with secure lids. The containers should be clearly marked and should be puncture resistant. 41. This paragraph best supports the idea that sanitation workers can be injured if they a. do not place sharp objects in punctureresistant containers. b. come in contact with sharp objects that have not been placed in secure containers. c. are careless with sharp objects such as lancets, needles, and syringes in their homes.

One of the missions of the Peace Corps is to bring trained men and women to work in countries who need trained professionals in certain fields. People who work for the Peace Corps are volunteers. However, in order to keep the Peace Corps dynamic and vital, no staff member can work for the agency for more than five years. 42. This paragraph best supports the statement that Peace Corps employees a. are highly intelligent people. b. must train for about five years. c. are hired for a limited term of employment. d. have both academic and work experience. More and more office workers telecommute from offices in their own homes. The benefits of telecommuting allow for greater productivity and greater flexibility. Telecommuters produce an average of 20% more than if they were to work in an office. In addition, their flexible schedules allow them to balance their families with their work responsibilities. 43. This paragraph best supports the statement that telecommuters a. get more work done in a given time period than workers who travel to the office. b. produce a better quality work product than workers who travel to the office. c. are more flexible in their ideas than workers who travel to the office. d. would do 20% more work if they were to work in an office.

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objective criteria. Hiring has to be based solely on a candidate’s knowledge, skills, and abilities— sometimes abbreviated as KSA—and not on external factors such as race, religion, or sex. Whereas employers in the private sector can hire employees for subjective reasons, federal employers must be able to justify their decision with objective evidence of candidate qualification.

Close-up images of Mars by the Mariner 9 probe indicated networks of valleys that looked like the stream beds on Earth. These images also implied that Mars once had an atmosphere that was thick enough to trap the Sun’s heat. If this is true, something must have happened to Mars billions of years ago that stripped away the planet’s atmosphere. 44. This paragraph best supports the statement that a. Mars once had a thicker atmosphere than Earth does. b. the Mariner 9 probe took the first pictures of Mars. c. Mars now has little or no atmosphere. d. Mars is closer to the Sun than Earth is. It is a myth that labor shortages today center mostly on computer jobs. Although it is true that the lack of computer-related skills accounts for many of the problems in today’s job market, there is a lack of skilled labor in many other fields. There is a shortage of uniformed police officers in many cities and a shortage of trained criminal investigators in some rural areas. These jobs may utilize computer skills, but they are not essentially computer jobs. 45. This paragraph best supports the statement that a. people with computer skills are in demand in police and criminal investigator jobs. b. unemployment in computer-related fields is not as widespread as some people think. c. there is a shortage of skilled workers in a variety of fields, including police work. d. trained criminal investigators are often underpaid in rural areas.

46. This paragraph best supports the statement that a. hiring in the private sector is inherently unfair. b. KSA is not as important as test scores to federal employers. c. federal hiring practices are simpler than those employed by the private sector. d. the civil service strives to hire on the basis of a candidate’s abilities. It is well known that the world urgently needs adequate distribution of food, but adequate distribution of medicine is just as urgent. Medical expertise and medical supplies need to be redistributed throughout the world so that people in emerging nations will have proper medical care. 47. This paragraph best supports the statement that a. the majority of the people in the world have no medical care. b. medical resources in emerging nations have diminished in the past few years. c. not enough doctors give time and money to those in need of medical care. d. many people who live in emerging nations are not receiving proper medical care.

The competitive civil service system is designed to give candidates fair and equal treatment and to ensure that federal applicants are hired based on

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Before you begin to compose a business letter, sit down and think about your purpose for writing the letter. Do you want to request information, order a product, register a complaint, or apply for something? Do some brainstorming and gather information before you begin writing. Always keep your objective in mind.

In the past, suggesting a gas tax has usually been considered a political blunder, but that does not seem to be the case today. Several states are promoting bills in their state legislatures that would cut income or property taxes and make up the revenue with taxes on fossil fuel. 48. This paragraph best supports the statement that a. gas taxes produce more revenue than income taxes. b. states with low income tax rates are increasing their gas taxes. c. state legislators no longer fear increasing gas taxes. d. taxes on fossil fuels are more popular than property taxes.

50. This paragraph best supports the statement that a. for many different kinds of writing tasks, planning is an important first step. b. business letters are frequently complaint letters. c. brainstorming and writing take approximately equal amounts of time. d. while some people plan ahead when they are writing a business letter, others do not.

Whether you can accomplish a specific goal or meet a specific deadline depends first on how much time you need to get the job done. What should you do when the demands of the job exceed the time you have available? The best approach is to divide the project into smaller pieces. Different goals will have to be divided in different ways, but one seemingly unrealistic goal can often be accomplished by working on several smaller, more reasonable goals. 49. This paragraph best supports the statement that a. jobs often remain only partially completed because of lack of time. b. the best way to complete projects is to make sure your goals are achievable. c. the best way to tackle large projects is to problem-solve first. d. the best approach to a demanding job is to delegate responsibility.

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Answers

1. d. By stating that fitness walking does not require a commute to a health club, the author stresses the convenience of this form of exercise. The paragraph also states that fitness walking will result in a good workout. Choice a is incorrect because no comparison to weight lifting is made. Choice b may seem like a logical answer, but the paragraph refers only to people who are fitness walkers, so for others, a health club might be a good investment. Choice c is not supported by the passage. 2. d. This answer is implied by the whole paragraph. The author stresses the need to read critically by performing thoughtful and careful operations on the text. Choice a is incorrect because the author never says that reading is dull. Choices b and c are not supported by the paragraph. 3. b. The last sentence in the paragraph clearly gives support for the idea that the interest in Shakespeare is due to the development of his characters. Choice a is incorrect because the writer never makes this type of comparison. Choice c is incorrect because even though scholars are mentioned in the paragraph, there is no indication that the scholars are compiling the anthology. Choice d is incorrect because there is no support to show that most New Yorkers are interested in this work. 4. a. The support for this choice is in the second sentence, which states that in some countries toxic insecticides are still legal. Choice b is incorrect because even though polar regions are mentioned in the paragraph, there is no support for the idea that warmer regions are not just as affected. There is no support for choice c. Choice d can be ruled out because

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5.

6.

7.

8.

9.

10. 11.

there is nothing to indicate that DDT and toxaphene are the most toxic insecticides. a. The second and third sentence combine to give support to choice a. The statement stresses that there must be a judge’s approval (i.e., legal authorization) before a search can be conducted. Choices b and d are incorrect because it is not enough for the police to have direct evidence or a reasonable belief—a judge must authorize the search for it to be legal. Choice c is not mentioned in the passage. b. This answer is clearly stated in the last sentence of the paragraph. Choice a can be ruled out because there is no support to show that studying math is dangerous. Choice d is a contradiction to the information in the passage. There is no support for choice c. d. The last sentence states that new technologies are reported daily, and this implies that new technologies are being constantly developed. There is no support for choice a. With regard to choice b, stone tools were first used two and a half million years ago, but they were not necessarily in use all that time. Choice c is incorrect because the paragraph states when stone tools first came into use. b. See the second and third sentences for the steps in making ratatouille. Only choice b reflects the correct order. d. The main part of the passage describes how to cook vegetables. Only choice d indicates that vegetables are included in the dish. The other choices are not reflected in the passage. d. The passage mentions nothing about main or secondary roads. a. The other choices may be true but are not mentioned in the passage.

–READING COMPREHENSION –

12. c. The passage indicates that the city prefers, but does not require, the use of the new containers. Also, customers may use more than one container if they purchase an additional one. 13. b. The passage states that the use of the new containers will expedite pick-up of recyclables. This indicates that the new containers will make the recycling program more efficient. 14. d. The mention that searching for spices has changed the course of history and that nations have gone to war over this condiment implies that the subject of the paragraph is history, not cooking, choices a, b, and c. The use of the word war involves danger and intrigue, so choice d is correct. 15. c. The mention of the amazing things the brain is capable of doing is directly relevant to its mysterious and complex nature. Choices a, b, and d are less relevant and specific. 16. b. Choice b addresses both of Gary’s vanities: his person and his situation. Choice a deals only with Gary’s vanity of person. Choice c deals only with his vanity of position. Choice d is not supported by the passage. 17. a. This choice refers both to age and complexity; choices b and c refer only to complexity. Choice d is less relevant to the topic sentence than the other choices. 18. d. Choice d reveals the fascination fans had with Marilyn. Choices a, b, and c are merely facts about Marilyn and are not about people’s fascination with her. 19. c. The topic sentence speaks of the big bang theory being much misunderstood, and choice c addresses this. The other choices are off topic. 20. a. This choice is a clear comparison between humans and birds: neither one needs

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21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

instruction to do what is important to its survival. Choices b, c, and d do not support this topic sentence. b. Because the wolves have produced more offspring than expected, chances are they will be taken off the endangered species list. Choices a, c, and d do not reinforce the context of the topic sentence. d. The topic sentence refers to punishment used in early America. Choice a gives a reason for the use of punishment by Puritans. Choices b and c state why you do not have such punishment today and compares historical punishment with today’s sensibility. d. The topic sentence states that violence has claimed many lives in Northern Ireland. Choices a, b, and c only show what led to the situation. c. This choice introduces the idea that some laws are strange. Choices a, b, and d are examples of strange laws, but not the topic sentence. a. This topic sentence states the importance of a cat’s whiskers. Choices b, c, and d give other details that do not directly support the topic sentence. c. This choice states the popularity of the game. Choices a and b state the game’s origin. Choice d explains how its popularity spread. c. This sentence gives a reason for why people are living longer. Choices a, b, and d are about longevity but are not topic sentences. a. Choice a pronounces an end to sixteen years of violence. Choice b, c, and d are facts about James’s life. O. This sentence is an opinion because it can be debated. Someone could just as easily take the opposite position. F. This sentence is a fact. It can proven.

–READING COMPREHENSION –

31. O. This sentence is an opinion. While it could be a good idea, there are no statistics to prove this. 32. F. This sentence is a fact. Wednesday is the fourth day of the week. 33. O. This sentence is an opinion. While Wednesday may seem longer to some people, it is the same length as any other day of the week. 34. F. This sentence is a fact. There are many opportunities for investment. 35. F. This sentence is a fact. People do invest in stocks and bonds. 36. O. This sentence is an opinion. Savings accounts and CDs do not always earn the highest interest rates. 37. F. This sentence is a fact. The stock market can be uncertain. 38. F. This sentence is a fact. Steady, secure interest can be earned using these methods of investing. 39. c. This sentence indicates the importance of organization and design. Choices a, b, and d, even if true, are not in the passage. 40. a. Choice a reflects the idea that the Dvorak keyboard is more efficient than the QWERTY. Choices b, c, and d are not in the passage. 41. b. Choice b is the only choice that tells how people should dispose of sharp objects in order to avoid placing sanitation workers in danger. Choices a, c, and d discuss how users should deal with sharp objects. 42. c. The last sentence of the passage supports choice c. Choices a, b, and d are not in the passage.

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43. a. Choice a details the greater productivity of telecommuters. Choices b, c, and d contain words and phrases from the paragraph, but are incorrect. 44. c. Choice c indicates that the atmosphere of Mars has been stripped away. 45. c. Choice c expresses the overall theme of the paragraph—a shortage of skilled workers in many fields. 46. d. Choice d is the best comprehensive statement about the paragraph. 47. d. Choice d is implied by the statement that redistribution is needed so that people in emerging nations can have proper medical care. Choices a, b, and c are not mentioned in the paragraph. 48. c. Choice c is the best answer because the paragraph indicates that legislators once feared suggesting gas taxes, but now many of them are promoting bills in favor of these taxes. There is no indication that choice a is true. Choice b is incorrect because the paragraph does not say why more gas taxes are being proposed. There is no support for choice d. 49. b. The passage is about making a larger goal more achievable by setting smaller goals. Only choice b mentions this. 50. a. Choice a is the best overall statement to summarize the message given by the paragraph. Choices b, c, and d do not support the main idea of the paragraph.

C H A P T E R

13

Grammar

T

he ability to write correctly is fundamental for any civil service position. This chapter reviews such grammar essentials as sentence boundaries, capitalization, punctuation, subject-verb agreement, verb tenses, pronouns, and commonly confused words. There is plenty of writing involved in most civil service jobs. Forms, memos, e-mails, letters, and reports have to be written during the course of every workday, and the grammar section of the written exam helps the government determine whether you have the competence it takes to complete such tasks. As you apply the vocabulary you have learned in this book, it is important to use these words correctly in sentences. Poor usage can get in the way of what you want to say. Correct usage of standard English shows that you have made the effort to understand the conventions of the English language. When English is used according to the conventions that have been established, your words allow the reader—and your employer or supervisor—to understand exactly what you intend to say. Studying the proper ways to use the vocabulary of the English language can give you a good score on the grammar section of the exam and will show that you are indeed capable and proficient as a writer. The tips and exercises in this chapter will help you ensure that you are ready to excel on this portion of the exam.

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–GRAMMAR–



Complete Sentences and Sentence Fragments

more is needed to complete the thought. These sentence fragments can easily be corrected:

Sentences are the basic units of written language. Complete sentences express a whole thought. They do not leave you guessing about who the subject is, or what action the subject is taking. When you are writing in the workplace, complete sentences are the correct and accepted format for most pieces of information. For that reason, it is important to distinguish between complete sentences and sentence fragments. A sentence expresses a complete thought, while a fragment is missing something—it could be a verb or it could be a subject, but the sentence does not express a complete thought. Look at the following examples. FRAGMENT

COMPLETE SENTENCE

The assistant

The assistant was

filing folders.

filing folders.

Leaving messages

Janet was always leaving

for me.

messages for me

The first fragment in this pair of sentences is an example of a sentence that is missing part of its verb. It needs the helping verb was before filing to make a complete thought. The second fragment has neither a subject nor a verb. Only when a subject and verb are added is this sentence complete. Look at the following incomplete sentences. When you saw the tornado approaching. Before the new house was built in 1972. Since you are leaving in the morning. You may have noticed that the fragments have an extra word at the beginning. These words are called subordinating conjunctions. When a group of words that would normally be a complete sentence is preceded by a subordinating conjunction, something

■

■

■

When you saw the tornado approaching, you headed for cover. Before the new house was built in 1972, the old house was demolished. Since you were leaving in the morning, you went to bed early.

Knowing that a subordinating conjunction can signal a sentence fragment, it is a good idea to be familiar with some of the most frequently used subordinating conjunctions. Then you can double-check your work for errors. Use this list as a handy reminder. after although as because before if once since than



that though unless until when whenever where wherever while

Run-On Sentences

Run-on sentences are two or more independent clauses (complete sentences) written as though they were one sentence. The main cause of run-on sentences is often faulty punctuation, such as a comma instead of a period between two independent clauses (complete thoughts). End marks like periods, exclamation points, and question marks can solve the runon sentence problem. Look at the following example.

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A complete report has to be submitted every week, it is due on Friday. This run-on sentence could be corrected in a few different ways. One way is to add a conjunction after the comma and in between the two independent clauses. Words such as and, or, but, as, or because are conjunctions that join sentences. Using the same sentence as a model, it would be considered correct if you wrote:



You may encounter questions on your civil service exam that test your ability to use capital letters correctly. If you know the most common capitalization rules, you will be better prepared to correct these errors. ■

■

A complete report has to be submitted every week, and it is due on Friday. It would also be correct to delete the comma and separate the two sentences with a semicolon. A semicolon indicates that the next part of the sentence is a complete sentence, but it is so closely related to the first that there is no reason to make it into a sentence of its own. So, it would be correct to say: A complete report has to be submitted every week; it is due on Friday. The sentence would be correct if you separated the two independent clauses to make two complete sentences. You could rewrite it as follows: A complete report has to be submitted every week. It is due on Friday. Last, the sentence would be correct if written with a dash: A complete report has to be submitted every week—it is due on Friday.

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Capitalization

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■

■

Capitalize the first word of a sentence. If the first word is a number, write it as a word. Capitalize the pronoun I. Capitalize the first word of a complete quotation: “What is the address?” she asked. However, do not capitalize the first word of a partial quotation: He called me “the best employee” and nominated me for an award. Capitalize proper nouns and proper adjectives. Proper nouns are names of people, places, or things, like Lyndon B. Johnson; Austin, Texas; or Mississippi River. They are different from common nouns like president, city, state, or river. Proper adjectives are adjectives formed from proper nouns. For instance, if the proper noun is Japan, the proper adjective would be Japanese language. If the proper noun is South America, the proper adjective would be South American climate. See the table that follows for examples of proper nouns and adjectives.

–GRAMMAR–

CATEGORY

EXAMPLE OF PROPER NOUNS

Days of the week

Friday, Saturday

Months of the year

January, February

Holidays

Christmas, Halloween

Special events

Two Rivers Festival, City Writers’ Conference

Names of individuals

John Henry, George Washington

Names of structures

Lincoln Memorial

Buildings

The Empire State Building

Names of trains

Orient Express

Ships

Queen Elizabeth II

Aircraft

Cessna

Product names

Honda Accord

Geographic locations (cities, states, counties,

Des Moines, Iowa

countries, and geographic regions)

Canada Middle East

Streets

Grand Avenue

Highways

Interstate 29

Roads

Dogwood Road

Landmarks

Continental Divide

Public areas

Grand Canyon, Glacier National Park

Bodies of water

Atlantic Ocean Mississippi River

Ethnic groups

Asian-American

Languages

English

Nationalities

Irish

Official titles (capitalized only when they appear

Mayor Bloomberg

before a person’s name—Marie Hanson,

President Johnson

president of the City Council, vs. City Council President Marie Hanson) Institutions

Dartmouth College

Organizations

Chrysler Corporation

Businesses

Girl Scouts

Proper adjectives (adjectives formed

English muffins, French cuisine

from proper nouns)

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Punctuation

■

A section on the written civil service exam may test your punctuation skills. Knowing how to correctly use periods, commas, and apostrophes will boost your score on the exam.

■

Periods

If you know the most common rules for using periods, you will have a much easier time spotting and correcting sentence errors. ■

■

Use a period at the end of a sentence that is not a question or an exclamation. Use a period after an initial in a name. ■ Example: John F. Kennedy

Use a period after an abbreviation, unless the abbreviation is an acronym. ■ Abbreviations: Mr., Ms., Dr., A.M., General Motors Corp.; Allied, Inc. ■ Acronyms: NASA, SCUBA, RADAR If a sentence ends with an abbreviation, use only one period. ■ Example: You brought pens, paper, pencils, etc.

Commas

Commas are more important than many people realize. The correct use of commas helps present ideas and information clearly to readers. Missing or misplaced commas, on the other hand, can confuse readers and convey a message quite different from what is intended. This chart demonstrates just how much impact commas can have on meaning.

There is an indeterminate number of people

My sister Diane John Carey Melissa and I

in this sentence.

went to dinner.

There are four people in this sentence.

My sister Diane, John Carey, Melissa, and I went to dinner.

There are five people in this sentence.

My sister, Diane, John Carey, Melissa, and I went to dinner.

There are six people in this sentence.

My sister, Diane, John, Carey, Melissa, and I went to dinner.

If you know the most common rules for using commas, you will have a much easier time identifying sentence errors and correcting them.

■

■ ■

Use a comma before and, but, so, or, for, nor, and yet when they separate two groups of words that could be complete sentences. Example: The manual listed the steps in sequence, and that made it easy for any reader to follow.

■

183

Use a comma to separate items in a series. Example: The student driver stopped, looked, and listened when she approached the railroad tracks. You may wonder if the comma after the last item in a series is really necessary. This is called a series comma, and is used to ensure clarity. Use a comma to separate two or more adjectives modifying the same noun. Example: The hot, black, rich coffee was just what I needed on Monday

–GRAMMAR–

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■

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morning. (Notice that there is no comma between rich—an adjective—and coffee—the noun it describes.) Use a comma after introductory words, phrases, or clauses in a sentence. Example of an introductory word: Usually, the secretary reads the minutes of the meeting. Example of an introductory phrase: During her lunch break, she went shopping. Example of an introductory clause: After you found the source of the problem, it was easily rectified. Use a comma after a name followed by Jr., Sr., M.D., Ph.D., or any other abbreviation. Example: The ceremony commemorated Martin Luther King, Jr. Remember that commas should be on both sides of an abbreviation—The life of Martin Luther King, Jr., was the subject of the documentary. Use a comma to separate items in an address. Example: The package was addressed to 1433 West G Avenue, Orlando, Florida 36890. Use a comma to separate a day and a year, as well as after the year when it is in a sentence. Example: I was born on July 21, 1954, during a thunderstorm. Use a comma after the greeting of a friendly letter and after the closing of a letter. Example of a greeting: “Dear Uncle John,.” Example of a closing: “Sincerely yours,.”

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■

Use a comma to separate contrasting elements in a sentence. Example: Your speech needs strong arguments, not strong opinions, to convince me. Use commas to set off appositives—words or phrases that explain or identify the noun in a sentence. Example: My dog, a dachshund, is named Penny.

Apostrophes

Apostrophes are used to show ownership or relationships, to show where letters have been omitted in a contraction, and to form the plurals of numbers and letters. If you know the most common rules for using apostrophes, you will have a much easier time spotting and correcting punctuation errors. ■

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■

Use an apostrophe in contractions. This tells the reader that a letter has been omitted. ■ Example: do not = don’t ■ I will = I’ll ■ it is = it’s Use an apostrophe to form the plural of numbers and letters. ■ Example: There are two o’s and two m’s in the word roommate. ■ She chose four a’s on the multiple choice exam. Use an apostrophe to show possession. USING APOSTROPHES TO SHOW

POSSESSION SINGULAR NOUNS RULE: ADD ’S

PLURAL NOUNS ENDING IN S RULE: ADD ’

PLURAL NOUNS NOT ENDING IN S RULE: ADD ’S

boy’s

boys’

men’s

child’s

kids’

children’s

lady’s

ladies’

women’s

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Verbs

The subject of a sentence—who or what the sentence is about, the person or thing performing the action— should agree with its verb in number. Simply put, this means that if a subject is singular, the verb must be singular; if the subject is plural, the verb must be plural. If you are unsure whether a verb is singular or plural, use this simple test. Fill in the blanks below using the verb speak. Be sure that it agrees with the subject. He . (The correct form of the verb in this sentence would be singular because the subject—he—is singular. The sentence, written correctly, would be: He speaks.) They . (The correct form of the verb in this sentence would be plural because the subject—they—is plural. The sentence, written correctly, would be: They speak.) Try this simple test with other verbs such as sing, write, think, or plan if you are confused about subject/verb agreement. Notice that a verb ending with s is usually a sign of the singular form of the verb, and there would be a singular subject in the sentence. Similarly, a subject ending with s is the sign of a plural subject, and the verb in the sentence would be plural. If a sentence includes a verb phrase (a main verb and one or more helping verbs), the helping verb (a verb that helps the main verb express action or make a statement) has to agree with the subject.

Agreement When Using Pronoun Subjects

Few people have trouble matching noun subjects and verbs, but pronouns are sometimes difficult for even the most sophisticated writers. Some pronouns are always singular; others are always plural. Still others can be either singular or plural, depending on the usage. These pronouns are always singular: each either neither anybody anyone everybody

everyone no one one nobody someone somebody

For example, you would say “Neither of them has been to Chicago”—not “Neither of them have been to Chicago.” Neither is the subject, so the verb must be singular. The indefinite pronouns each, either, and neither are most often misused. You can avoid a mismatch by mentally adding the word one after the pronoun and removing the other words between the pronoun and the verb. Look at the following examples. Each of the men wants his own car. Each one of the men wants his own car.

Example: The gymnast is performing. The gymnasts are performing.

Either of the sales clerks knows where the sale merchandise is located. Either one of the sales clerks knows where the sale merchandise is located.

The new schedule has interfered with our plans. The new schedules have interfered with our plans.

It is important to note that a subject is never found in a prepositional phrase. Any noun or pronoun found in a prepositional phrase is the object of the preposition, and this word can never be the subject of

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the sentence. Try to filter out prepositional phrases when looking for the subject of a sentence. Using the two sentences as models, note the prepositional phrases in bold. When you have identified these phrases, you will have a much easier time finding the subject of the sentence. Each of the men wants his own car. Either of the sales clerks knows where the sale merchandise is located.



many several

He and she want to buy a new house. Bill and Verna want to buy a new house.



He or she wants to buy a new house. He wants to buy a new house. She wants to buy a new house.

none some

The words or prepositional phrases following these pronouns determine whether they are singular or plural. If what follows the pronoun is plural, the verb must be plural. If what follows is singular, the verb must be singular. All of the work is finished. All of the jobs are finished. Is any of the pizza left? Are any of the pieces of pizza left?

Agreement When Using Subjects Joined by or or nor

If two nouns or pronouns are joined by or or nor, they require a singular verb. Think of them as two separate sentences, and you will never make a mistake in agreement.

Other pronouns can be either singular or plural: all any most

Agreement When Using Subjects Joined by and

If two nouns or pronouns are joined by and, they require a plural verb.

These kinds of sentences may sound awkward because many speakers misuse these pronouns, and you may be used to hearing them used incorrectly. To be sure that you are using them correctly, the substitution trick—inserting one for the words following the pronoun—will help you avoid making an error. Some pronouns are always plural and require a plural verb. They are: both few

None of the time was wasted. None of the minutes were wasted.

Neither Portuguese nor Dutch is widely spoken today. Portuguese is not widely spoken today. Dutch is not widely spoken today.



Verb Tense

The tense of a verb tells the reader when the action occurs, occurred, or will occur. Present tense verbs let the reader imagine the action as it is being read. Past tense verbs tell the reader what has already happened. Future tense verbs tell the reader what will happen.

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sented one city block. Street names were labeled. Arrows on streets indicated that the street was one way only in the direction of the arrow. Twoway traffic was allowed on streets with no arrows. This plan alleviated traffic in the downtown area. 3. To plan for growth in the small city, a city planner will be hired. The city planner will present a map of the city where some public buildings will be located. Each of the squares on the map will represent one city block. Street names will be labeled. Arrows on streets will indicate that the street will be one way only in the direction of the arrow. Two-way traffic will be allowed on streets with no arrows. This plan will alleviate traffic in the downtown area.

Read the three paragraphs that follow. The first is written in the present tense, the second in the past tense, and the third in the future tense. Notice the difference in the verbs; they are highlighted so that you can easily see them. 1. To plan for growth in the small city, a city planner is hired to speak to the town council. The city planner presents a map of the city where some public buildings are located. Each of the squares on the map represents one city block. Street names are labeled. Arrows on streets indicate that the street is one way only in the direction of the arrow. Two-way traffic is allowed on streets with no arrows. This plan alleviates traffic in the downtown area. 2. To plan for growth in the small city, a city planner was hired. The city planner presented a map of the city where some public buildings were located. Each of the squares on the map repre-

It is easy to distinguish present, past, and future tense by trying the word in a sentence beginning with today (present tense), yesterday (past tense), or tomorrow (future tense).

PRESENT TENSE TODAY, I

PAST TENSE YESTERDAY, I

FUTURE TENSE TOMORROW, I

drive

drove

will drive

think

thought

will think

rise

rose

will rise

catch

caught

will catch

The important thing to remember about verb tense is to be consistent. If a passage begins in the present tense, keep it in the present tense unless there is a specific reason to change—to indicate that some action occurred in the past, for instance. If a passage begins in

the past tense, it should remain in the past tense. Similarly, if a passage begins in the future tense, it should remain in the future tense. Verb tense should never be mixed as it is in the following sample.

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Incorrect The doorman opens the door and saw the crowd of people. Correct Present Tense: The doorman opens the door and sees the crowd of people. Past Tense: The doorman opened the door and saw the crowd of people. Future Tense: The doorman will open the door and will see the crowd of people. Sometimes it is necessary to use a different verb tense in order to clarify when an action took place. Read the following sentences and their explanations.

The director rode with Jerry and I. Belle and him are going to the company picnic. The errors in these sentences are not as easy to spot as those in the sentences using a single pronoun. In order to remedy this problem, you can turn the sentence with two pronouns into two separate sentences. Then the error becomes very obvious. The director rode with Jerry. The director rode with me (not I).

1. The game warden sees the fish that you caught. (The verb sees is in the present tense and indicates that the action is occurring in the present. The verb caught is in the past tense and indicates that the fish were caught at some earlier time.) 2. The house that was built over a century ago sits on top of the hill. (The verb was built is in the past tense and indicates that the house was built in the past. The verb sits is in the present tense and indicates that the action is still occurring.)



sentence, she should be her. Such errors are easy to spot when the pronouns are used alone in a sentence. The problem occurs when a pronoun is used with a noun or another pronoun. See if you can spot the errors in the following sentences.

Belle is going to the company picnic. He (not him) is going to the company picnic.

Pronouns

Using a single pronoun in a sentence is usually easy to do. In fact, most people would readily be able to identify the mistakes in the following sentences. Me went to the movie with he. My instructor gave she a ride to the class. Most people know that me in the first sentence should be I and that he should be him. In the second

To help you move through this grammar problem with ease, you should know that subject pronouns—those that are the subject in a sentence or the predicate nominative—are in the nominative case. (A predicate nominative is a noun or pronoun that is the same as the subject. For example: It was I. In this sentence, the subject it is the same as the pronoun I.) Subjective pronouns are I, he, she, we, and they. Objective pronouns—those that are the object of a preposition or the direct/indirect object of the sentence—are in the objective case. (A direct object is the word that receives the action of the verb or shows the result of the action. It answers the question who or whom. For example: She went with me. An indirect object is the word that comes before the direct object. It tells to whom or for whom the action of the verb is done. For example: She gave me some flowers on my birthday.)

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If he and she want to join us, they are welcome to do so. Mark and Jennifer planned a meeting to discuss their ideas.

Objective pronouns are me, him, her, us, and them. You and it do not change their forms, so there is no need to memorize case for those words. Knowing when to use objective pronouns can become problematic when they are used in compounds such as: She directed her comments to Margaret and me. A simple way to find the correct pronoun is to test each one separately.

If two or more singular nouns or pronouns are joined by or, use a singular pronoun. If a singular and a plural noun or pronoun are joined by nor, the pronoun should agree with the closest noun or pronoun it represents. The bank or the credit union can lend money to its patrons. The treasurer or the assistant will loan you his calculator.

She directed her comments to Margaret. She directed her comments to me.



Pronoun Agreement

Using singular and plural pronouns can be a problem at times. Like subjects and verbs, pronouns must match the number of the nouns they represent. If the noun that a pronoun represents is singular, the pronoun must be singular. On the other hand, if the noun a pronoun represents is plural, the pronoun must be plural. Sometimes a pronoun represents another pronoun. If so, either both pronouns must be singular or both pronouns must be plural.Consult the lists of singular and plural pronouns you saw earlier in this chapter. The doctor must take a break when she is tired. (singular) Doctors must take breaks when they are tired. (plural) One of the girls misplaced her purse. (singular) All of the girls misplaced their purses. (plural)

Neither the soldiers nor the sergeant was sure of her location. Neither the sergeant nor the soldiers was sure of their location.



Commonly Confused Words

The following word pairs are often misused in written language. By reading the explanations and looking at the examples, you can learn to use these words correctly every time. Its/It’s Its is a possessive pronoun and shows that something belongs to it. It’s is a contraction for it is or it has. The only time you should ever use it’s is when you can also substitute the words it is or it has.

If two or more singular nouns or pronouns are joined by and, use a plural pronoun to represent them.

189

The dog knows its way home. It’s only fair that I should do the dishes for you tonight.

–GRAMMAR–

Who/That Who refers to people. That refers to things. There is the man who helped me find my wallet. The office worker who invented White-Out was very creative.

Your/You’re Your is a possessive pronoun that means something belongs to you. You’re is a contraction for the words you are. The only time you should use you’re is when you can substitute the words you are. Your name will be the next one called. You’re the next person to be called.

This is the house that my sister bought. The book that I need is no longer in print. There/Their/They’re Their is a possessive pronoun that shows ownership. There is an adverb that tells where an action or item is located. They’re is a contraction for the words they are. It is easy to remember the differences if you remember these tips. ■

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■

Their means belonging to them. Of the three words, their can be most easily transformed into the word them. Extend the r on the right side and connect the i and the r to turn their into them. This clue will help you remember that their means that it belongs to them. ■ Their coats should be hanging on racks by the door. If you examine the word there, you can see that it contains the word here. Whenever you use there, you should be able to substitute here, and the sentence should still make sense. ■ She told me to wait over there for the next available salesperson. Imagine that the apostrophe in they’re is actually a very small letter a. Use they’re in a sentence only when you can substitute they are. ■ Yes, they’re coming to dinner with us next Saturday night.

To/Too/Two To can be used as a preposition or an infinitive. ■

■

A preposition shows relationships between other words in a sentence. ■ Example: My car is in the employee parking lot. The word in shows the relation of my car to parking lot. The meaning of the sentence would be different if another preposition such as on, over, or beside were used. Other examples: to the office, in the red, to my home, beside the table, over the top, at his restaurant, to our disadvantage, in an open room, by the door An infinitive is to followed by a verb. For example: to talk, to deny, to see, to find, to advance, to read, to build, to want, to misinterpret, to peruse ■ Example; To find the correct answer, I did some very careful thinking.

Too means also. To see if you are using the correct spelling of the word too, substitute the word also. The sentence should still make sense. Example: I did not know that you wanted to go too. Too can also mean excessively. It was too hot inside the car. Two is a number, as in one, two. If you memorize this, you will never misuse this form. There are only two people in our party.

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Practice Questions

For questions 1–8, look for run-on sentences or sentence fragments. Choose the answer choice that does NOT express a correct, complete sentence. If there are no mistakes, select choice d.

5. a. What is the best route to Philadelphia? b. The artichokes cost more than the asparagus does. c. Turn off the television it’s time for dinner! d. no mistakes. 6. a. Baseball is the national pastime of the United States. b. Ernest Hemingway won the Nobel Prize for Literature. c. The rest of the story coming to you later. d. no mistakes.

1. a. Manuel wanted to complete all of his courses so he could get his degree. b. She couldn’t believe the premise of the story. c. The train leaving the station. d. no mistakes

7. a. b. c. d.

2. a. At the end of the day, they hoped to be finished with all tasks. b. When will you teach me how to cook like you do? c. I can’t wait Janet can’t either. d. no mistakes

The sky was a brilliant blue this morning. John is an avid stamp collector. Elvis Presley’s home is in Memphis, Tennessee. no mistakes

8. a. If you see a grizzly bear, do not make any sudden movements. b. The county executive a person who works very hard. c. The national park system in the United States preserves land for all to enjoy. d. no mistakes

3. a. The medieval literature class was very interesting. b. The children in the park, including all of the girls on the swings. c. Christina is an excellent elementary school teacher. d. no mistakes

For questions 9–13, choose the sentence that uses commas correctly.

4. a. Sandra Day O’Connor was the first woman to serve on the U.S. Supreme Court. b. You visited the presidential library of Lyndon B. Johnson. c. I saw Dr. Sultana because Dr. Das was on vacation. d. no mistakes.

9. a. b. c. d.

191

Ecstatic the winner, hugged her coach. My best friend, James is always on time. As far as I know, that room is empty. Maureen my cousin, is going to Hawaii in August.

–GRAMMAR–

10. a. Concerned about her health, Jessica made an appointment to see a doctor. b. Those sneakers are available in black tan red, and white. c. After, checking our equipment you began our hiking trip. d. Exhausted I climbed, into bed. 11. a. Hoping for the best, I called Dan. b. You visited England, France Spain, and Italy. c. You can have chocolate ice cream or, you can have a dish of vanilla pudding. d. Timothy, however will attend a community college in the fall. 12. a. Max was the most physically fit and he won the 5K, race. b. Shortly she will answer, all messages. c. My physician, Dr. O’Connor, told me I was very healthy. d. Bonnie was outgoing friendly, and sociable. 13. a. After his vacation to the Caribbean Art, decided to learn scuba diving. b. I like jazz, classical, and blues music. c. My good friend, Melanie sent me a picture of her new puppy. d. The abundant, blue, violets were scattered everywhere in the woodland garden.

For questions 14–19, choose the sentence or phrase that has a mistake in capitalization or punctuation. If you find no mistakes, select choice d. 14. a. My favorite season is Spring. b. Last Monday, Aunt Ruth took me shopping. c. You elected Ben as treasurer of the freshman class. d. no mistakes 15. a. He shouted from the window, but you couldn’t hear him. b. NASA was launching its first space shuttle of the year. c. The boys’ wore identical sweaters. d. no mistakes 16. a. Occasionally someone will stop and ask for directions. b. When you come to the end of Newton Road, turn left onto Wilson Street. c. Lauren’s father is an auto mechanic. d. no mistakes 17. a. That book must be yours. b. This is someone elses coat. c. Don B. Norman was one of the founders of the community. d. no mistakes 18. a. The US flag should be flown proudly. b. She served eggs, toast, and orange juice for breakfast. c. He wanted turkey, lettuce, and mayonnaise on his sandwich. d. no mistakes

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For questions 20–25, choose the correct verb form.

24. The people who bought this old lamp at the antique auction very smart. a. was b. were c. is d. has been

20. I am trying to become more skilled at weaving before winter a. arrived. b. will have arrived. c. will arrive. d. arrives.

25. I her speak on Friday night about the advantages of organic gardening. a. will have heard b. would hear c. would have heard d. will hear

21. While trying to his cat from a tree, he fell and hurt himself. a. be rescuing b. have rescued c. rescue d. rescuing

For questions 26–30, choose the correct pronoun form.

19. a. b. c. d.

Dear Anne, Sincerely, yours Yours truly, no mistakes

26. That snappy looking sports car belongs to my sister and . a. I b. me c. mine d. myself

22. The volunteers from the fire department quickly and extinguished a fire on North Country Road. a. will respond b. responded c. will have responded d. have responded

27. The person cious cheesecake has my vote. a. that b. which c. who d. whose

23. In Tuesday’s paper, the owner of the supermarket was recognized for helping a customer who on the icy sidewalk. a. falls b. would fall c. had fallen d. has fallen

28. George and Michael left backpacks in the car. a. his b. their c. there d. its

193

made this deli-

–GRAMMAR–

34. a. That parrot doesnt talk. b. Don’t spend too much money. c. You waited until he stopped to make a phone call. d. no mistakes

29. You arranged the flowers and placed in the center of the table. a. them b. this c. it d. that 30.

met more than ten years ago at a mutual friend’s birthday party. a. Her and I b. Her and me c. She and me d. She and I

For questions 31–40, find the sentence that has a mistake in grammar or usage. If there are no mistakes, select choice d. 31. a. b. c. d.

Have you ever read the book called The Firm? She urged me not to go. Stop, look, and listen. no mistakes

32. a. Three’s a crowd. b. If you’re not sure, look in the dictionary. c. They weren’t the only ones that didn’t like the movie. d. no mistakes 33. a. Anne will leave first and Nick will follow her. b. Maya Angelou, a famous poet, recently spoke at our school. c. The clerk asked for my address and phone number. d. no mistakes

35. a. b. c. d.

Alberto laughed loudly when he saw us. They’re looking for another apartment. The first house on the street is there’s. no mistakes

36. a. b. c. d.

I love the fireworks on the Fourth of July. The dog’s barking woke us from a sound sleep. My grandparents live in Dallas, Texas. no mistakes

37. a. b. c. d.

Ursula has broke one of your plates. The sun rose from behind the mountains. Don’t spend too much time on that project. no mistakes

38. a. She believed in keeping a positive attitude. b. After you sat down to eat dinner, the phone rung. c. Sign all three copies of the form. d. no mistakes 39. a. The Adirondack Mountains are in New York. b. President Carter returned control of the Panama Canal to Panama. c. She missed the bus and arrives late. d. no mistakes

194

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40. a. The childrens books are over there. b. There is not enough paper in the printer for the entire document. c. What’s the weather forecast for today? d. no mistakes

45. a. They are the ones who deserve all the credit. b. This is the house that I told you about. c. Marie sent a gift to her grandmother, who is in the hospital. d. no mistakes

For questions 41–45, choose the sentence that does not use the correct form of the commonly confused word. If there are no mistakes, select choice d.

For questions 46–50, choose the sentence that is correct in both grammar and punctuation.

41. a. If it’s nice weather tomorrow, I plan to go for a hike. b. Some analysts think the stock market has seen it’s best days. c. It’s usually a good idea to purchase life insurance. d. no mistakes 42. a. She spoke too quickly to the group in the lobby. b. Can you attend this morning’s meeting too? c. Save all of your files in to or three folders. d. no mistakes 43. a. When will you bring you’re pictures to work? b. It is your responsibility to arrange the details. c. If you’re planning to attend, please let me know in advance. d. no mistakes 44. a. Only their supervisor can answer those questions. b. There is a phone call for you. c. They’re are only two ways to handle that situation. d. no mistakes

46. a. The trip was scheduled for Friday the family was excited. b. The trip was scheduled for Friday, and the family was excited. c. The trip was scheduled for. Friday the family was excited. d. The trip, was scheduled for Friday, and the family was excited. 47. a. They finished their lunch. Left the building. And returned at 1:30. b. They finished their lunch, left the building, and returns at 1:30. c. They finished their lunch, left the building, and returned at 1:30. d. They finished their lunch, left the building, and returning at 1:30. 48. a. Searching for her keys, Kira, knew she would be late. b. Searching for her keys Kira knew she would be late. c. Searching, for her keys and Kira knew she would be late. d. Searching for her keys, Kira knew she would be late.

195

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49. a. The longtime residents in the community were proud of there school district. b. The longtime residents in the community were proud of their school district. c. The longtime residents in the community was proud of their school district. d. The longtime residents in the community, were proud of their school district.

50. a. Lisa, Dara, and Amy wanted to work together on the committee. b. Lisa Dara and Amy wants to work together on the committee. c. Lisa, Dara, and Amy wanting to work together on the committee. d. Lisa, Dara, and Amy have wants to work together on the committee.

196

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Answers

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.

27. c. The correct pronoun is who because it refers to a person. 28. b. The pronoun their agrees with the plural subject, George and Michael. 29. a. The pronoun them agrees with the plural noun flowers. 30. d. She and I is the subject of the sentence, so the subjective case is needed. 31. d. There are no mistakes. 32. c. The word that should be who because it refers to people. 33. a. There should be a comma before the conjunction and in this sentence to separate two complete thoughts. 34. a. The contraction doesn’t should have an apostrophe. 35. c. The correct possessive pronoun is theirs, not there’s. 36. d. There are no mistakes. 37. a. The correct verb form is has broken. 38. b. The correct verb form is rang. 39. c. Both verbs, missed and arrives should be in the past tense. 40. a. An apostrophe should be added before the s in children’s to make it possessive. 41. b. This sentence requires the possessive form (with no apostrophe), its. 42. c. The required form of this word is the number two. 43. a. This sentence should use the possessive form of the word your. 44. c. This sentence should use the adverb there. 45. d. There are no mistakes. 46. b. This choice uses the comma and the conjunction correctly. Choice a is a run-on sentence. Choice c contains sentence fragments. Choice d misuses commas.

c. This is a sentence fragment. c. This is a run-on sentence. b. This is a sentence fragment. d. There are no mistakes. c. This is a run-on sentence. c. This is a sentence fragment. d. There are no mistakes. b. This is a sentence fragment. b. The commas set off an introductory phrase. a. The comma sets off an introductory clause. a. The comma sets off an introductory phrase. c. The comma sets off the appositive in the sentence. b. The commas separate items in a series. a. Spring should not be capitalized. c. The word boys’ should not show possession; no apostrophe is needed. a. A comma is need to set off the introductory word, occasionally. b. An apostrophe is needed before the last s in the word elses to show possession. a. There should be periods after the abbreviation U.S. b. The comma should be placed after the word yours. d. This sentence is in the present tense. c. The infinitive form of the verb is used in this sentence. b. This sentence is in the past tense. c. This sentence needs a verb that is in the past tense. b. Were is in agreement with the plural subject people. d. This sentence is in the future tense. b. The correct form of the pronoun is me (objective case).

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47. c. The word returned is in the past tense, as are finished and left. Choice a contains sentence fragments. Choices b and d misuse verb tense. 48. d. The comma in this sentence correctly separates the introductory phrase. Choices a and c misuse commas. Choice b lacks punctuation. 49. b. This sentence uses the correct form of their, the correct verb, and the correct punctuation.

198

The word there is used incorrectly in choice a. Choice c uses verb tense incorrectly. Choice d is an example of comma misuse. 50. a. This sentence uses the correct punctuation in a series and the correct verb form. Choices b, c, and d misuse commas and verb tense.

C H A P T E R

14

Spelling

B

ecause accurate spelling is such an essential and important communication skill, it is always tested on the civil service exam. In this chapter, you will find spelling rules, test tips, and practice exercises that will make the spelling section of the exam easier for you. There is no “quick fix” for spelling. The secret to correct spelling is memorization. If you take the time to commit the words you encounter every day to memory, not only will you excel on this section of the exam, but your correspondence and written work will be more clear and effective and look more professional. Spelling tests are usually given in multiple-choice format. Typically, you will be given several possible spellings for a word and asked to identify the one that is correctly spelled. This can be a difficult task, even for the best speller, because you must be able to see very subtle differences between word spellings. The best way to prepare for a spelling test is to put your memorization skills into high gear, have a good grasp of spelling rules, and know the exceptions to those rules. The fundamental rules and their exceptions are outlined here.

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–SPELLING–

SPELLING RULES AND EXCEPTIONS THE RULE

Use i before e—as in piece.

THE EXCEPTION

Use i before e except after c—as in receive or conceive—or when ei sounds like a—as in neighbor or weigh.

When adding prefixes, do not change the spelling

none

of the word—as in unnecessary or misspell When adding suffixes, do not change the spelling

When a word ends in y, change the y to i before

of the word—as in finally or usually.

adding ness or ly—as in heaviness or readily. One-syllable words ending in y generally remain the same—as in dryness or shyly.

Drop the final e before adding a suffix that begins

Keep the final e to retain the soft sound of c or g

with a vowel—as in caring or usable.

preceding the e—as in noticeable or courageous.

Keep the final e before a suffix beginning with

Words like truly, argument, judgment, or

a consonant—as in careful or careless.

acknowledgment are exceptions.

When words end in y and a consonant precedes

none

the y, change the y to i before adding a suffix with i—as in hurried or funnier. When a suffix begins with a vowel, double the

If the accent is not on the last syllable, do not add a

final consonant before the suffix if the word

double consonant—as in canceled or preferable.

has only one syllable—as in planning—or if the word ends with a single consonant preceded by a single vowel—as in forgetting. When spelling the plural form of a noun,

none

add an s—as in books or letters. add an es—as in boxes or lunches. Nouns are normally made plural by adding an s. An es is added when there is an extra sound heard in words that end in s, sh, ch, or x—as in dresses, birches, bushes, or boxes. If the noun ends in a y, change the y to an i and

If the noun ends in y and is preceded by a vowel,

add es—as in salaries or ladies.

just add s—as in attorneys or monkeys.

If a noun ends in f or fe, add an s

Some nouns that end in f or fe are formed by changing

—as in chiefs or roofs.

the f to v and adding s or es—as in knives or leaves.

200

–SPELLING–

THE RULE

THE EXCEPTION

If a noun ends in o and is preceded by a vowel,

Some nouns that end in o preceded by a consonant

add an s—as in pianos or radios

are formed by adding es—as in potatoes or tomatoes.

Plural or compound nouns can be spelled with

Some plural nouns are irregular nouns and have to be

an s or an es—as in bookmarks or mailboxes.

memorized—as in children, men, or women.

When a noun and a modifier make a compound

A few compound nouns are irregular—as in six year olds

noun, the noun is made plural—as in

or drive-ins. Some nouns take the same form in the

sisters-in-law or passers-by.

singular and the plural—as in deer, species, or sheep.

Numbers, letters, signs, and words that take the

none

shape of words are spelled with an apostrophe and an s—She received all A’s on her report card or There are two o’s and two m’s in roommate. Some foreign words are formed as they are in their original language—as in alumni or data. Some foreign words may be spelled as they are in the original language or by adding s or es—as in appendixes/appendices or indexes/indices. Some foreign words are formed according to the ending of the word: *singular ending in is plural ending in es—as in analysis/analyses or crisis/crises. *singular ending in um plural ending in a—as in curriculum/curricula. *singular ending in on plural ending in a—as in criterion/criteria. *singular ending in eau plural ending in eaux—as in beau/beaux. *singular ending in a plural ending in ae—as in formula/formulae. *singular ending in us plural ending in i—as in stimulus/stimuli. When using -cede, -ceed, or -sede, memorize the following: There is only one English word ending in sede—supersede. There are only three common verbs ending in ceed—exceed, proceed, and succeed. Other words that have the same sound end in cede—secede, precede, and concede, for example.

201

Shortcut—How to Answer Spelling Questions ■

Sound out the word in your mind. Remember that long vowels inside words usually are followed by single consonants—as in sofa, total, or crime. Short vowels inside words usually are followed by double consonants—as in dribble, scissors, or toddler.

■

Give yourself auditory (listening) clues when you learn words. Say Wed-nes-day or lis-ten or bus-i-ness to yourself so that you remember to add the silent letters when you write the word.

■

Look at each part of the word. See if there is a root, prefix, or suffix that will always be spelled the same way. For example, in the word uninhabitable, un, in, and able are always spelled the same. Habit is a selfcontained root word that is easy to spell.

Memorize as many spelling rules as you can and know the exceptions to the rules.



Using Spelling Lists

When you apply to take your civil service exam, you may be given a list of spelling words to study. If so, here are some suggestions to make your studying a little easier and quicker. ■

■

■

■

■

Cross out or discard any words that you already know for certain. Do not let them get in the way of the words you need to study. Divide the list into groups to study. The groups can be bunched as three, five, or seven words. Consider making flash cards for the words that you find the most difficult. Say the words as you read them. Spell them out in your mind so you can “hear” the spelling. Highlight or circle the tricky elements in each word. Quiz yourself and then check your spelling.

If you do not receive a list of spelling words to study, the following list is a good one to use. These words are typical of the words that appear on spelling exams.

202

achievement

doubtful

ninety

allege

eligible

noticeable

anxiety

enough

occasionally

appreciate

enthusiasm

occurred

asthma

equipped

offense

arraignment

exception

official

autonomous

fascinate

pamphlet

auxiliary

fatigue

parallel

brief

forfeit

personnel

ballistics

gauge

physician

barricade

grieve

politics

beauty

guilt

possess

beige

guarantee

privilege

business

harass

psychology

bureau

hazard

recommend

calm

height

referral

cashier

incident

rehearsal

capacity

indict

salary

cancel

initial

schedule

–SPELLING–

circuit

innocent

seize

colonel

irreverent

separate

comparatively

jeopardy

specific

courteous

knowledge

statistics

criticism

leisure

surveillance

custody

license

suspicious

cyclical

lieutenant

tentative

debt

maintenance

thorough

definitely

mathematics

transferred

descent

mortgage

withhold



Homophones

Words that sound alike but have different meanings are called homophones or homonyms. The following chart shows some of the most common homophones for you to study. It is best to study the spellings and the definitions until you have each word memorized.

HOMOPHONES

ad: a shortened form of advertisement add: to combine to form a sum affect: to influence effect: outcome or result allowed: permitted aloud: using a speaking voice bare: without covering bear: a large furry animal; to tolerate board: a group of people in charge; a piece of wood bored: to be tired of something brake: to slow or stop something break: to split or crack build: to construct billed: presented a statement of costs cite: to quote as an authority or example sight: ability to see; a scene site: place or setting of something

203

–SPELLING–

council: a group that advises counsel: advice; to advise dew: moisture do: to make or carry out due: owed fair: consistent with the rules; having a pleasing appearance; moderately good fare: transportation charge; food and drink; to get along for: because of or directed to fore: located at or toward the front four: a number between three and five grate: reduce to fragments; make a harsh, grinding sound; irritate or annoy great: very large in size hear: to listen to here: a specific place heard: the past tense of hear herd: a large group of animals hole: an opening whole: entire or complete hour: 60 minutes our: a pronoun showing possession knew: past tense of know new: recent know: to understand no: not permitted lead: first or foremost position; a margin; information pointing toward a clue led: past tense of lead leased: rented for a specific time period least: lowest in importance or rank lessen: made fewer in amount or quantity lesson: exercise in which something is learned made: past tense of make maid: a servant meat: the edible part of an animal meet: come together

204

–SPELLING–

passed: the past tense of pass past: previous, beforehand peace: free from war piece: a part of something plain: level area; undecorated; clearly seen plane: flat and even; a tool used to smooth wood; a shortened form of airplane rain: water falling in drops reign: period during which a monarch rules right: correct or proper rite: a ritual or ceremony write: to record in print role: function or position; character or part played by a performer roll: to move forward by turning over scene: the place something happens seen: form of the verb see soar: to fly or rise high into the air sore: painful stair: part of a flight of steps stare: to look directly and fixedly sweet: having a sugary taste suite: series of connected rooms their: ownership of something there: a place they’re: a contraction of they are threw: the past tense of throw; an act of motion through: by means of; among or between tide: variation of the level of bodies of water caused by gravitational forces tied: the past tense of tie to: indicates direction too: also two: the number after one vary: to change very: complete; extremely

205

–SPELLING–

ware: articles of the same general kind, e.g., hardware, software wear: to have or carry on the body where: location or place weather: condition of the atmosphere whether: a possibility wood: material that trees are made of would: form of the verb will



Practice Questions

4. It was a annual picnic. a. superb b. supperb c. supurb d. sepurb

For questions 1–14, choose the correctly spelled word. 1. It is my that municipal employees handle their jobs with great professionalism. a. beleif b. bilief c. belief d. beleaf 2. The accounting firm was fraudulent practices. a. prosecuted b. prossecuted c. prosecutted d. prosecuited 3. Every a. sittuation b. situation c. situachun d. sitiation

day for the department’s

5. To be elected , candidates must have a solid background in law enforcement. a. sherrif b. sherriff c. sherif d. sheriff

for

has to be handled differently.

6. To be hired for the job, he needed to have ability. a. mechinical b. mechanical c. mechenical d. machanical 7. The agents were searching for cargo on the airplane. a. elicitt b. ellicit c. illicet d. illicit

206

–SPELLING–

8. There will be an immediate the cause of the accident. a. inquiry b. inquirry c. enquirry d. enquery

13. The attorney asked a question that was to the case; the judge overruled it. a. irelevent b. irelevant c. irrelevant d. irrelevent

into

14. The mayor highlighted the tics during her campaign speech. a. encouredging b. encouraging c. incurraging d. incouraging

9. The union workers’ contract could not be before the calendar year ended. a. terminated b. termenated c. terrminated d. termanated 10. A a. b. c. d.

can be obtained at the town hall. lisense lisence lycence license

11. In many states, passing a road test requires drivers to park. a. paralel b. paralell c. parallal d. parallel 12. The paramedics attempted to victim. a. stabilize b. stablize c. stableize d. stableise

the

statis-

For questions 15–36, choose the misspelled word. If there are no mistakes, select choice d. 15. a. b. c. d.

radios leaves alumni no mistakes

16. a. b. c. d.

anouncement advisement description no mistakes

17. a. b. c. d.

omission aisle litrature no mistakes

18. a. b. c. d.

informal servent comfortable no mistakes

207

–SPELLING–

19. a. b. c. d.

vegetable width variation no mistakes

27. a. b. c. d.

quantaty quality quaint no mistakes

20. a b. c. d.

twentieth fortieth ninetieth no mistakes

28. a. b. c. d.

requirement reverence resistent no mistakes

21. a. b. c. d.

association unecessary illegal no mistakes

29. a. b. c. d.

incorporate contridict exhale no mistakes

22. a. b. c. d.

villin volunteer voracious no mistakes

30. a. b. c. d.

pertain reversel memorization no mistakes

23. a. b. c. d.

hindrence equipped possessive no mistakes

31. a. b. c. d.

marshal martial tyrenny no mistakes

24. a. b. c. d.

procedure judgment testamony no mistakes

32. a. b. c. d.

optimum palpable plunder no mistakes

25. a. b. c. d.

explicit abduct rotate no mistakes

33. a. b. c. d.

ravinous miraculous wondrous no mistakes

26. a. b. c. d.

through threw thorough no mistakes

208

–SPELLING–

34. a. b. c. d.

phenomonal emulate misconception no mistakes

35. a. b. c. d.

mischief temperture lovable no mistakes

36. a. b. c. d.

stadium competitor atheletic no mistakes

41. Come to see the sunset. a. buy b. bye c. by 42. This is the a. fourth b. forth

the park later this evening

book George has read.

43. The acoustics in the auditorium made it easy for the audience to the melodic sounds of the soloist. a. here b. hear

For the questions 37–50, choose the correct homophone. 37. My favorite vanilla ice cream. a. desert b. dessert

44. Our choice to stay in the comfortable, cozy house was a good decision. a. guessed b. guest

is peach pie with

38. While nuclear energy is efficient, storing nuclear is always a problem. a. waste b. waist

45. Have dinner with us at the restaurant; we’ll meet you . a. they’re b. their c. there

39. The price for the carpet was a. fair b. fare

46. May I have a a. piece b. peace

40. This is the a. sight b. cite c. site

.

of the new art museum.

47. All children have the education. a. write b. rite c. right

209

of cheese?

to an

–SPELLING–

48. It is a good idea to exercise on a bicycle during inclement weather. a. stationery b. stationary

50. We around. a. past b. passed

49. At the beach, we went digging for clams and . a. mussels b. muscles

210

the exit and had to turn

–SPELLING–



Answers

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.

33. 34. 35. 36. 37.

c. belief a. prosecuted b. situation a. superb d. sheriff b. mechanical d. illicit. This word should not be confused with elicit, which means to draw out or extract. a. inquiry a. terminated d. license d. parallel a. stabilize c. irrelevant b. encouraging d. no mistakes a. announcement c. literature b. servant d. no mistakes d. no mistakes b. unnecessary a. villain a. hindrance c. testimony d. no mistakes d. no mistakes a. quantity c. resistant b. contradict b. reversal c. tyranny d. no mistakes

38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.

211

a. ravenous a. phenomenal b. temperature c. athletic b. Dessert is an after-dinner treat; a desert is an arid land. a. Waste means material that is rejected during a process; the waist is the middle of the body. a. Fair means equitable; a fare is a transportation fee. c. Site refers to a place; cite means to refer to; sight is the ability to see. c. By means near; bye is used to express farewell; buy means to purchase. a. Fourth refers to the number four; forth means forward. b. Hear means to perceive sound with the ear; here is a location, place, or position. b. A guest is one who is a recipient of hospitality. Guessed is the past tense of guess. c. There refers to a place; their is a possessive pronoun; they’re is a contraction for they are. a. A piece is a portion; peace means calm or quiet. c. A right is a privilege; to write is to put words on paper; a rite is a ceremonial ritual. b. Stationary means standing still; stationery is writing paper. a. Mussels are marine animals; muscles are body tissues. b. Passed is the past tense of pass; past means a time gone by.

S E C T I O N

4

Test Time!

D

on’t close this book and run away just yet. “Test time” should not be a phrase that inspires sweaty palms and nervous stomachs. The practice tests in this section are intended to gauge your skills before you sit down to take the civil service exam. By knowing in what areas you are strong and in what areas you are rusty, you will be better prepared on the day of the official civil service exam. Like any scout will tell you, it’s best to be prepared! After reviewing Sections 1 through 3 in this book, you should be able to put all that you have learned together and tackle these questions. Allow yourself about two hours to complete Practice Test 1. After you are done, be sure to check your answers against the answer section. Then, reevaluate questions you answered incorrectly by going back and studying the necessary material from earlier chapters. You can make flashcards for math formulas or tricky vocabulary concepts. Then try your skills again—take Practice Test 2. Again, if there are topics with which you are not comfortable, make sure you review these sections before the official test day. Good luck!

213

C H A P T E R

15

Practice Test 1

215

––PRACTICE TEST 1––

5. During a relay race, markers will be placed along a roadway at 0.2-mile intervals. If the entire roadway is 10,560 feet long, how many markers will be used? a. 10 b. 100 c. 20 d. 200

1. If a piece of packaging foam is .05 in. thick, how thick would a stack of 350 pieces of foam be? a. 7,000 in. b. 700 in. c. 175 in. d. 17.5 in. 2. 30% of what number equals 60% of 9,000? a. 18,000 b. 5,400 c. 2,400 d. 1,620

6. If it takes 27 nails to build 3 boxes, how many nails will it take to build 7 boxes? a. 64 b. 72 c. 56 d. 63

3. Three pieces of wood measure 4 yd. 1 ft. 3 in., 5 yd. 2 ft. 4 in., and 4 yd. 1 ft. 5 in. lengthwise. When these boards are laid end to end, what is their combined length? a. 14 yd. 2 ft. b. 14 yd. 1 ft. 11 in. c. 13 yd. 2 in. d. 13 yd. 2 ft.

7. The average purchase price (arithmetic mean) of four shirts is $9. If one shirt was priced at $15, and another at $7, what might be the prices of the other two shirts? a. $4 and $3 b. $7 and $15 c. $9 and $9 d. $10 and $4

4. Select the answer choice that best completes the following sequence.

8. What percent of 38 is 12? a. 25% b. 3313% c. 75% d. 13313%

a. b. c. d.

9. A large bag of cement mix weighs 3812 pounds. How many quarter-pound bags of mix can be made from this large bag? a. fewer than 10 bags b. 16 bags c. 80 bags d. 154 bags

217

–PRACTICE TEST 1–

10. Use (F = 95 C + 32) to convert 15o C into the equivalent Fahrenheit temperature. a. 59o b. 60o c. 62o d. 65o 11. What is the perimeter of the shaded area if the shape is a quarter circle with a radius of 8?

a. b. c. d.

2 4 2 + 8 4 + 16

12. Select the answer choice that best completes the following sequence. CMM, EOO, GQQ, , KUU a. GRR b. GSS c. ISS d. ITT 13. How many ounces are in 5 pints? a. 10 oz. b. 20 oz. c. 40 oz. d. 80 oz.

15. Joel had to insert form letters into 800 envelopes. In the first hour he completed 81 of the total. In the second hour he completed 72 of the remainder. How many envelopes does he still have to fill? a. 300 b. 400 c. 500 d. 700 16. Jen’s median bowling score is greater than her mean bowling score for 5 tournament games. If the scores of the first four games were 140, 192, 163, and 208, which could have been the score of her fifth game? a. 130 b. 145 c. 168 d. 177 17. An 18-gallon barrel of liquid will be poured into containers that each hold half a pint of fluid. If all of the containers are filled to capacity, how many will be filled? a. 36 b. 72 c. 144 d. 288 18. Select the answer choice that best completes the sequence.

14. A rod that is 3.5 × 107 cm is how much shorter than a rod that is 7 × 1014 cm? a. 20,000,000 times shorter b. 4,000,000 times shorter c. 50,000 times shorter d. 20,000 times shorter

a. b. c. d.

218

––PRACTICE TEST 1––

23. If the area of a circle is 16 square inches, what is the circumference? a. 2 inches b. 4 inches c. 8 inches d. 12 inches

19. In a box of 300 nails, 27 are defective. If a nail is chosen at random, what is the probability that it will NOT be defective? a. b. c. d.

27  10 0 91  10 0 27  30 0 91  30 0

20. When Christian and Henrico work together, they can complete a task in 6 hours. When Christian works alone, he can complete the same task in 10 hours. How long would it take for Henrico to complete the task alone? a. 45 b. 30 c. 15 d. 10 21. The square root of 52 is between which two numbers? a. 6 and 7 b. 7 and 8 c. 8 and 9 d. none of the above 22. Juliet made $12,000 and put 34 of that amount into an account that earned interest at a rate of 4%. After 3 years, what is the dollar amount of the interest earned? a. $10,080 b. $10,800 c. $1,800 d. $1,080

24. Select the answer choice that best completes the sequence. QAR, RAS, SAT, TAU, a. UAV b. UAT c. TAS d. TAT 25. A container was filled 13 of the way with fluid. Damian added 24 liters more, filling the container to full capacity. How many liters are in the container now? a. 12 L b. 30 L c. 36 L d. 48 L 26. Bolts cost $4 per 10 dozen and will be sold for 10 cents each. What is the rate of profit? a. 200% b. 150% c. 100% d. 75%

219

–PRACTICE TEST 1–

29. Which of the following statements appears to be true for the years shown? a. The fox population doubled every year since 2004. b. The deer population doubled every year since 2005. c. The owl population showed neither a steady increase nor a steady decrease. d. Both b and c are true.

27. Select the answer choice that best completes the sequence.

a. b. c. d.

28. $6,000 is deposited into an account. If interest is compounded semiannually at 2% for 6 months, then what is the new amount of money in the account? a. $120 b. $6,120 c. $240 d. $6,240 Use the following information to answer questions 29–32.

Number of animals

A forest fire engulfed the Wildlife Preserve in Blackhill County in 2003. Since then, park rangers have kept track of the number of forest animals living in the forest. The following is a graph of how many deer, foxes, and owls were reported during the years following the fire. 80 70 60 50 40 30 20 10 0

deer foxes

30. Which statement might explain the data presented in the graph? a. The owl population was greatly reduced by the fire and thus the trend shows a steady increase in this population during the years of recovery. b. The owls were able to fly away from the fire, thus the owl population does not show the pattern of recovery that the deer and fox population exhibit. c. Factors independent of the fire are causing a steady decline in the owl population. d. A steep decline in the owl population can be attributed to illness. 31. The growth of the deer population from 2006–2007 was how much greater than the growth of the fox population for the same year? a. 10 b. 20 c. 30 d. 40

owls

2004

2005 Year

2006

2007

32. What was the percent increase in deer from 2004–2005? a. 3313% b. 50% c. 34% d. 13%

220

––PRACTICE TEST 1––

33. A square with 8 in. sides has the same area of a rectangle with a width of 4 in. What is the length of the rectangle? a. 8 in. b. 12 in. c. 16 in. d. 64 in.

37. The following chart shows the monthly attendance for union meetings over the course of four months. Which two months had the same number of members attending? 50 40 30 20 10

34. A rectangular tract of land measures 440 feet by 1,782 feet. What is the area in acres? (1 acre = 43,560 square feet.) a. 14 acres b. 16 acres c. 18 acres d. 20 acres

0

a. b. c. d.

Nov

Dec

Jan

Feb

November and December December and February November and February December and January

35. What is the mode of the following numbers? 12, 9, 8, 7, 8, 9, 5, 9 a. 7 b. 8.375 c. 9 d. 9.5

38. If the radius of a cylindrical tank is 7 cm and its volume is 1,540 cm3, what is the height in cm? a. 10 cm b. 15.4 cm c. 10 cm d. 15.4 cm

36. The largest sector of the pie chart below has a central angle equal to approximately how many degrees?

39. If Martin exchanges 120 quarters, 300 dimes, 600 nickels, and 500 pennies for bills, he may get a. 4 20-dollar bills, 2 10-dollar bills, and 1 5dollar bill. b. 3 20-dollar bills, 1 10-dollar bill, and 1 5dollar bill. c. 2 50-dollar bills and 1 20-dollar bill. d. 1 50-dollar bill, 2 20-dollar bills, and 1 5dollar bill.

a. b. c. d.

15 degrees 45 degrees 90 degrees 180 degrees

40. Brian jogged 12 miles. For the first 2 miles, his pace was 3 mph. For the next 3 miles, his pace was 5 mph. For the remainder of his jog, his pace was 4 mph. What was his approximate average speed? a. 3.98 mph b. 6.86 mph

221

–PRACTICE TEST 1–

c. 7.2 mph d. 223 mph Choose the correct vocabulary word to complete each of the following sentences. 41. The newspaper the statement made in the article because it was incorrectly stated. a. abolished b. invalidated c. retracted d. annulled 42. The proposition was read, and the committee was asked to vote on the issue; Connor decided to from the vote. a. tackle b. undermine c. abstain d. destabilize 43. Typically, computer designs reach within six months. a. division b. discord c. obsolescence d. secrecy

45. The new senator was considered a because she refused to follow her party’s platform on nearly every issue. a. mentor b. maverick c. protagonist d. visionary 46. School calendars were originally based on a(n) lifestyle, where all family members needed to be available to help in the fields. a. business b. technological c. scientific d. agrarian 47. The project seemed both and beneficial, and the office staff supported it enthusiastically. a. implacable b. feasible c. savory d. irreparable

44. For information about making a sound investment, you should get advice from a(n) . a. prospectus b. entrepreneur c. teller d. cashier

222

––PRACTICE TEST 1––

48. Judith, a young worker, diligently replaced all of the research files at the end of every day. a. erudite b. insightful c. meticulous d. sagacious

53. Choosing to her estate to the literacy foundation, she was able to help those who could not read. a. confiscate b. eliminate c. bequeath d. extract

49. His behavior made him seem childish and immature. a. beguiling b. receding c. forlorn d. puerile

54. Her haughty and manner was not appealing to her constituents. a. poignant b. nocturnal c. amicable d. supercilious

50. The young woman gave generously to many worthy causes. a. incisive b. benevolent c. gregarious d. personable

55.

51.

donations from a generous but anonymous benefactor were received every year at the children’s hospital. a. Magnanimous b. Parsimonious c. Prudent d. Diplomatic

, the pediatric nurse fed the Read the passage and respond to the questions that follow.

premature baby. a. Carelessly b. Precariously c. Gingerly d. Wantonly 52. The furniture in the attic turned out to be a veritable of valuable antiques. a. reproof b. bonanza c. censure d. rubble

223

Today, bicycles are elegantly simple machines that are common all over the globe. Many people ride bicycles for recreation while others use them as a means of transportation. The first bicycle, called a draisienne, was invented in Germany in 1818 by Baron Karl de Draid de Sauerbrun. Because it was made of wood, the draisienne was not very durable, nor did it have pedals. Riders moved it by pushing their feet against the ground. In 1839, Kirkpatrick Macmillan, a Scottish blacksmith, invented a much better bicycle. Macmillan’s machine had tires with iron rims to keep them from getting worn down. He also used foot-operated cranks similar to pedals so his bicycle could be

–PRACTICE TEST 1–

ridden at a quick pace. It did not look much like the modern bicycle because its back wheel was substantially larger than its front wheel. Although Macmillan’s bicycle could be ridden easily, they were never produced in large numbers. In 1861, Frenchman Pierre Michaux and his brother Ernest invented a bicycle with an improved crank mechanism. They called their bicycle a velocipede, but most people called it a bone shaker because of the jarring effect of the wood and iron frame. Despite the unflattering nickname, the velocipede was a hit and the Michaux family made hundreds of the machines annually. Most of them were for fun-seeking young people. Ten years later, James Starley, an English inventor, made several innovations that revolutionized bicycle design. He made the front wheel many times larger than the back wheel, put a gear on the pedals to make the bicycle more efficient, and lightened the wheels by using wire spokes. Although this bicycle was much lighter and less tiring to ride, it was still clumsy, extremely top-heavy, and ridden mostly for entertainment. It was not until 1874 that the first truly modern bicycle appeared on the scene. Invented by another Englishman, H. J. Lawson, this safety bicycle would look familiar to today’s cyclists. The safety bicycle had equalized wheels, which made it much less prone to toppling over. Lawson also attached a chain to the pedals to drive the rear wheel. By 1893, the safety bicycle had been further improved with airfilled rubber tires, a diamond-shaped frame, and easy braking. With the improvements provided by Lawson, bicycles became extremely popular and useful for transportation. Today they are built, used, and enjoyed all over the world.

56. There is enough information in this passage to show that a. several people contributed to the development of the modern bicycle. b. only a few velocipedes built by the Michaux family are still in existence. c. for most of the nineteenth century, few people rode bicycles just for fun. d. bicycles with wheels of different sizes cannot be ridden easily. 57. The first person to use a gear system on bicycles was a. H. J. Lawson. b. Kirkpatrick Macmillan. c. Pierre Michaux. d. James Starley. 58. This passage was most likely written in order to a. persuade readers to use bicycles for transportation. b. describe the problems that bicycle manufacturers encounter. c. compare bicycles used for fun with bicycles used for transportation. d. tell readers a little about the history of the bicycle. 59. Macmillan added iron rims to the tires of his bicycle to a. add weight to the bicycle. b. make the tires last longer. c. make the ride less bumpy. d. made the ride less tiring.

224

––PRACTICE TEST 1––

60. Read the following sentence from the fourth paragraph: Ten years later, James Starley, an English inventor, made several innovations that revolutionized bicycle design. As it is used in the sentence, the word revolutionized most nearly means a. canceled. b. transformed. c. maintained. d. preserved.

64. An antonym for deterrent is a. encouragement. b. obstacle. c. proponent. d. discomfort.

61. Which of the following statements from the passage represents the writer’s opinion? a. The safety bicycle would look familiar to today’s cyclists. b. Two hundred years ago, bicycles did not even exist. c. The Michaux brothers called their bicycle a velocipede. d. Macmillan’s machine had tires with iron rims.

66. A synonym for animated is a. abbreviated. b. civil. c. secret. d. lively.

Read the directions for each of the following questions and select the word that is the synonym or antonym for the word provided. 62. A synonym for apathetic is a. pitiable. b. indifferent. c. suspicious. d. evasive. 63. A synonym for surreptitious is a. expressive. b. secretive. c. emotional. d. artistic.

65. An antonym for impertinent is a. reverential. b. rude. c. relentless. d. polite.

67. A synonym for augment is a. repeal. b. evaluate. c. increase. d. criticize. 68. An antonym for ludicrous is a. absurd. b. somber. c. reasonable. d. charitable. 69. An antonym for archaic is a. tangible. b. modern. c. ancient. d. haunted.

225

–PRACTICE TEST 1–

70. A synonym for vindictive is a. outrageous. b. insulting. c. spiteful. d. offensive. Answer each of the following grammar and usage questions. 71. Which of the following sentences uses the correct pronoun form? a. Do you think you will work with Jason or I on this project? b. Do you think you will work with Jason or me on this project? c. Do you think you will work with Jason or she on this project? d. Do you think you will work with Jason or he on this project? 72. Which of the following sentences is correctly punctuated? a. Charlotte, who ran in the Boston Marathon last year will compete in this years New York City Marathon. b. Charlotte who ran in the Boston Marathon, last year, will compete in this year’s New York City Marathon. c. Charlotte who ran in the Boston Marathon last year, will compete in this years New York City Marathon. d. Charlotte, who ran in the Boston Marathon last year, will compete in this year’s New York City Marathon.

73. Which of the following sentences is capitalized correctly? a. The Governor gave a speech at the fourth of July picnic, which was held at morgan’s beach. b. The Governor gave a speech at the Fourth of July picnic, which was held at Morgan’s beach. c. The governor gave a speech at the Fourth of July picnic, which was held at Morgan’s Beach. d. The governor gave a speech at the fourth of july picnic, which was held at Morgan’s Beach. 74. Which of the following sentences uses the correct verb form? a. Before I learned to read, my sister takes me to the public library. b. Before I learned to read, my sister will take me to the public library. c. Before I learned to read, my sister took me to the public library. d. Before I learned to read, my sister has took me to the pubic library. 75. Which of the following sentences shows subject/verb agreement? a. The art professor, along with several of her students, is planning to attend the gallery opening tomorrow evening. b. The art professor, along with several of her students, are planning to attend the gallery opening tomorrow evening. c. The art professor, along with several of her students, plan to attend the gallery opening tomorrow evening. d. The art professor, along with several of her students, have planned to attend the gallery opening tomorrow evening.

226

––PRACTICE TEST 1––

76. In which of the following sentences is the verb NOT in agreement with the subject? a. Where are the forms you want me to fill out? b. Which is the correct form? c. Here is the forms you need to complete. d. There are two people who still need to complete the form. 77. In which of the following sentences is the pronoun NOT correct? a. Francine can run much faster than me. b. Erin and Bob are painting the house by themselves. c. Five members of the team and I will represent our school. d. Our neighbors gave us some tomatoes from their garden. 78. Which of the following sentences uses the correct verb form? a. Only one of the many problems were solved. b. Only one of the many problems was solved. c. Only one of the many problems been solved. d. Only one of the many problems are solved. 79. Which of the following sentences uses punctuation correctly? a. Dr. Richard K Brown, CEO of the company, will speak to the scientists at Brookhaven National Laboratory on Wed at 9:00 A.M. b. Dr Richard K Brown, C.E.O. of the company, will speak to the scientists at the Brookhaven National Laboratory on Wed. at 9:00 A.M. c. Dr. Richard K. Brown, C.E.O. of the company, will speak to the scientists at the Brookhaven National Laboratory on Wed. at 9:00 A.M. d. Dr. Richard K. Brown, C.E.O. of the company, will speak to the scientists at the Brookhaven National Laboratory on Wed at 9:00 A.M.

80. Which of the following sentences is NOT a runon sentence? a. He was from a small town, he moved to a very large city. b. He was from a small town he moved to a very large city. c. He was from a small town, but he moved to a very large city. d. He was from a small town but he moved to a very large city. Choose the correctly spelled word to complete each of the following sentences. 81. Each of the new employees has similar . a. asspirations b. asparations c. aspirrations d. aspirations 82. The president and the vice president were a pair. a. compatible b. compatable c. commpatible d. compatibel 83. I was skeptical of the claims made by the salesman. a. loquatious b. loquacious c. loquacius d. loquecious

227

–PRACTICE TEST 1–

84. Who is your immediate a. supervisor b. supervizor c. superviser d. supervizer 85. There are two types of viral and bacterial. a. neumonia b. pnumonia c. pnemonia d. pneumonia

?

:

Choose the misspelled word in the following questions. If there are no mistakes, select choice d. 86. a. b. c. d.

illuminate enlighten clarify no mistakes

87. a. b. c. d.

abolish forfit negate no mistakes

88. a. b. c. d.

zoology meterology anthropology no mistakes

89. a. b. c. d.

ajournment tournament confinement no mistakes

90. a. b. c. d.

vague trepidation vengence no mistakes

228

––PRACTICE TEST 1––



Answers

1. d. To solve, multiply the thickness of each piece of foam by the total number of pieces; .05  350 = 17.5 in. 2. a. “30% of what number equals 60% of 9,000?” can be written mathematically as .30 × x = .60 × 9,000. Dividing both sides by .30 will yield x (.60)(9,000) 5,400  = .3 0 =  .30 .30 = 18,000 3. a. First, line up all of the units and add: 4 yd. 1 ft. 3 in. 5 yd. 2 ft. 4 in. + 4 yd. 1 ft. 5 in. 13 yd. 4 ft. 12 in. Next, note that 12 in. = 1 ft., so 13 yd. 4 ft. 12 in. is the same as 13 yd. 5 ft., and that 3 ft. = 1 yd., so 5 ft. = 1 yd. + 2 ft. Ultimately, you can rewrite the entire length as 14 yd. 2 ft. 4. d. The amount of the shaded area changes from 1 1 1      4 2 4 Thus, you need to find the answer that is 14 shaded followed by 12 shaded. Choice d is correct. 5. a. 5,280 feet = 1 mile, so 10,560 feet = 2 miles. To solve, divide the total 2 mile distance by the interval, .2 miles: 2 ÷ .2 = 10. 6. d. First set up a proportion: 237 = 7x. You can reduce the first fraction: 91 = 7x and then cross multiply: 1(x) = 9(7), so x = 63. 7. d. If the cost of four shirts averaged out to $9, then the sum of all four shirts was 4 × 9 = $36. (Note that the sum of all 4 shirts must equal $36 in order for the average to equal 9: Average = sum ÷ 4 = 36 ÷ 4 = 9.) Of the $36 total, $22 is accounted for (one shirt was $15, and another $7), leaving $14 unaccounted for. Only choice d adds to $14.

229

8. d. Recall that “What percent” can be expressed x 3 1 as  10 0 . The question “What percent of 8 is 2?” x 3 1 can be expressed as:  10 0 × 8 = 2. This simpli3×x 1 fies to  800 = 2. Cross multiplying yields 6 × x = 800. Dividing both sides by 6 yields x = 13313%. 9. d. Divide 3812 by 14. By expressing 3812 as its equivalent 38.5, you get: 38.5 ÷ 14 = 38.5 × 41 = 154 bags. 10. a. Substitute 15o C in for the variable C in the given equation. Thus, F = 95C + 32 becomes F = 95(15) + 32 = (9)(3) + 32 = 27 + 32 = 59 degrees Fahrenheit. 11. d. The perimeter of the curved length is a quarter of the circumference of a whole circle when r = 8. Since C = 2r and you want a quarter of this value, solve 14 × 2 ×  × r = 14 × 2 ×  × 8 = 4. The two straight edges are radii and are each 8 units long. Thus, the total perimeter = 4 + 8 + 8 = 4 + 16. 12. c. The first letter of each triplet changes by skipping 1 letter : C  E  G  I  K. Thus, the first letter in the missing triplet is I. The last 2 letters of each triplet follow the same pattern (skip 1 letter): MM  OO  QQ  SS  UU. Thus, the answer is ISS. 13. d. Using the knowledge that 1 pt. = 2 c. and 1 c. = 8 oz., you can use a series of conversion factors to eliminate pints and keep ounces. Thus, 2 c. 8 oz.  you multiply: 5 pt. ×  1 p t. ×  1 c. = 80 oz. 14. a. To find how many “times shorter” the first 7 × 1014 rod is, divide:  3.5 × 107 14 – 7 = 2  10 = 2 × 107 = 20,000,000 times shorter. Hint: Treat their division like two separate division operations, 7 ÷ 3.5 and 1014 ÷ 107. But you must remember that the dividends

–PRACTICE TEST 1–

15.

16.

17.

18.

19.

are multiplied together in the end. Also, to divide 1014 by 107, subtract the exponents. c. Joel starts with 800 envelopes to fill. During the first hour he filled 18 of the 800: 18 × 800 = 100. He then had 800 – 100 = 700 left to fill. In the second hour he filled 27 of the remaining 700; 27 × 700 = 200 filled in the second hour. After two hours, Joel has 700 – 200 = 500 remaining. d. The mean is found by adding up the numbers and dividing by the number of values. The median is found by listing all of the numbers in order and taking the middle value. To find the solution, try out each answer choice to see if it works. A score of 130 would give a mean of 167 and a median of 163. A score of 145 would give a mean of 169 and a median of 163. A score of 168 would give a mean of 174 and a median of 168. A score of 177 would give a mean of 176 and a median of 177. 177 is the only one that has a median greater than the mean: Median = 140 163 177 192 208 Mean = (140 + 163 + 177 + 192 + 208) ÷ 5 = 880 ÷ 5 = 176 d. Using the knowledge that 1 gal. = 4 qt. and 1 qt. = 2 pt., you can generate a series of conversion factors and multiply them so that you can cross out the units you do not want (gal.) and keep the units you do want (pt.): 18 gal. 4 qt. 2 pt.  × 1 g al. ×  1 qt. = 144 pints. Next, remember you are looking for half-pints. 144 pints will fill 288 half-pint containers. d. This is an alternating series. The first and third segments are repeated. The second segment is a reverse of the other two. b. If 27 of the 300 are defective, then 300 – 27 = 273 are not defective. Thus, the probability of selecting a nail that is not defective will be

230

20.

21. 22.

23.

24.

25.

273 out of 300: 91 273  =  10 0 300 c. Christian can complete 110 of the task in 1 hour (you assume this because he completes the entire task in 10 hours). Together, Christian and Henrico complete 16 of the task in 1 hour. Convert both fractions into thirtieths. 5 3 3 0 per hour (both men) – 3 0 per hour (just 2 1 Christian) = 30 = 15 per hour (just Henrico). Since Henrico completes 115 of the task per hour, it will take him 15 hours to complete the entire task when working alone. b. 72 = 49 and 82 = 64. So the square root of 52 will equal a number that is between 7 and 8. d. Use the formula I = PRT, which means Interest = principal × rate of interest × time, where principal equals your original amount of money (in dollars), and time is in years. Here the original amount of money (P) is $9,000 because she put 34 of the $12,000 into the account. I = .04 and T = 3 years. Substituting into I = PRT, you get I = (9000)(.04)(3) = $1,080. c. You are told that Area = 16 . Since A = r2, 16 = r2 , and r = 4. Use this r in the circumference formula: Circumference = C = 2r = 2 × 4 = 8 inches. a. The first letter in each triplet progresses from Q  R  S  T, so the next triplet will begin with U. The second letter of each triplet is a constant: A. The third letter of each triplet progresses from R  S  T  U, so the third letter in the next triplet will be V. Thus, the answer is UAV. c. 24 L represents 23 of the whole capacity. You can ask yourself “23 of what number is 24?” This can be expressed mathematically as 23 × x = 24; x = 24 ÷ 23 = 24 × 32 = 36 L.

––PRACTICE TEST 1––

26. a. 10 dozen bolts = 10 × 12 = 120 bolts. When they are all sold, the amount collected is $.10 × 120 = $12. Since the 10 dozen cost $4, the profit is $12 – $4 = $8. Next, to find the rate of profit, set up a proportion: $8 profit x   =  initial $4 100 Cross multiply to get (100)(8) = (4)(x), or 800 = (4)(x). Divide both sides by 4 to get x = 200. Thus, the rate of profit is 200%. 27. a. As the series progresses, the amount of shading changes from 12  34  whole  none  1 1 3       whole. So the next two terms 4 2 4 will be: none  14. 28. b. Because the interest is compounded semiannually (twice a year), after half a year (6 months) the amount of interest earned I = PRT = 6,000 × .02 × 12 = $120. Now the account has $6,000 + $120 = $6,120 in it. 29. d. The fox population (lightest bars) went up by 10 animals each year. Thus, choice a is incorrect. The deer population (black bar) doubled every year since 2005 (20  40  80). The owl population stayed around 30, showing neither an increase nor a decrease. Thus, both b and c are true statements, making choice d, “Both b and c are true,” the correct answer. 30. b. The owl population is essentially maintaining its size. There is not a steady increase (a is incorrect), a steady decline (c is incorrect), or a steep decline (d is incorrect). Thus, choice b is the correct answer. 31. c. The deer (black bar) went from 40 in 2006 to 80 in 2007. That is an increase of 40 deer. The fox population (lightest bar) grew from 30 in 2006 to 40 in 2007. That is an increase of 10. Thus the difference in growth is 40 – 10 = 30. 32. a. The deer (black bar) increased from 15 in 2004 to 20 in 2005. This is a change of 5 deer.

231

33.

34.

35.

36.

37.

38.

39.

When compared to the initial 15, 5 out of 15 x 1 represents 155 =  10 0 ; x = 333%. c. The area of the square is A = side2 = s2 = 82 = 64 in.2. The area of the rectangle must then also be 64 in.2. Substituting this area and the given width w = 4 into the area formula, you get: A = lw; 64 = l × 4 ; l = 64 ÷ 4 = 16 in. c. First, calculate the area in square feet: Area = lw = 440 ft. × 1782 ft. = 784,080 ft.2. Next convert to acres by using the conversion fac1 acre 2 tor  43,56 0 ft.2 and multiply: 784,080 ft. × 1 acre  43,56 0 ft.2 = 18 acres. c. The mode is the number that occurs the most. You are given: 12, 9, 8, 7, 8, 9, 5, 9. Note that 9 occurs the most and is the mode. c. The largest sector takes up a quarter of the pie chart (the black sector). The interior angles of a circle add to 360 degrees and 14 of 360 = 14 × 360 = 90 degrees. c. The attendance for both November and February was 20 members each. You can tell that this is true because the bars for these months are the same height. a. If you use  = 272 , and the formula V =  r2h, you get 1,540 = 272 × 72 × h. This simplifies to 1,540 = 154 × h. Dividing both sides by 154 yields h = 10 cm. d. Multiply the number of coins by the value of the coin: 120 quarters = 120 × $.25 = $30 300 dimes = 300 × $.10 = $30 600 nickels = 600 × $.05 = $30 500 pennies = 500 × $.01 = $5 Next, add all of the dollar amounts up: $30 + $30 + $30 + $5 = $95. The only choice that represents $95 is d: 1 50-dollar bill, 2 20-dollar bills, and 1 5-dollar bill.

–PRACTICE TEST 1–

40. b. To find the average speed, you must use D = RT (Distance = Rate (Time) with the total distance and the total time as D and T respectively. You are given the total distance of 12 miles. You need the total time. This can be found by using the information in the question. The formula D = RT can be rewritten as T = DR. Making a chart for yourself will help you stay organized: INFO

TIME

2 mi. @ 3 mph

2 40    T = D R = 3 = 60

3 mi. @ 5 mph

3 36    T = D R = 5 = 60

7 mi. @ 4 mph

7 105    T = D R = 4 = 60 181  Total time =  60 hr ≈ 3.02 hr

41.

42. 43. 44. 45. 46. 47. 48.

Now you can use the total time and total distance in the formula D = RT. Since you want R, you can rearrange this formula to R = D ÷ T. Thus, you have R = D ÷ T = 12 ÷ 3.02 hr ≈ 3.98 mph. c. To retract something is to take it back or disavow it. This is the term usually applied to withdrawing something erroneous or libelous printed in a newspaper. c. To abstain means to refrain from something by one’s own choice. c. Obsolescence is the state of being outdated. a. A prospectus is a published report of a business and its plans for a program or offering. b. A maverick is a political independent, nonconformist, or free spirit. d. Agrarian means having to do with agriculture or farming. b. To be feasible is to be practical, manageable, convenient, or serviceable. c. Meticulous means extremely and excessively concerned with details.

232

49. d. Puerile means to be of or like a child; to be boyish, trifling, or silly. 50. b. A benevolent person is one who is charitable, giving. 51. c. To handle a baby gingerly would be to handle it delicately and with great caution. 52. b. A bonanza is a source of great wealth or prosperity. 53. c. To bequeath something is to pass it to another when you die. 54. d. To be supercilious means to show arrogant superiority and disdain for those one views as unworthy. 55. a. Magnanimous donations are noble in mind or heart. 56. a. Each paragraph of the passage describes an inventor whose inventions became more and more advanced. There is no evidence to support choice b. Choices c and d are incorrect because they both make statements that, according to the passage, are untrue. 57. d. The fourth paragraph states that James Starley added a gear to the pedals. 58. d. The passage gives the history of the bicycle. Choice a is incorrect because few opinions are included in the passage. There is no support for choices b and c. 59. b. This information is clearly stated in the second paragraph. The iron rims kept the tires from wearing down, and the tires lasted longer. Choice a is incorrect because although the iron rims probably did make the machine heavier, that was not Macmillan’s goal. Choice c is incorrect because no information is given about whether iron-rimmed or wooden tires moved more smoothly. There is no support for choice d. 60. b. Based on the paragraph, this is the only possible choice. Starley revolutionized the bicycle;

––PRACTICE TEST 1––

61.

62.

63. 64. 65. 66. 67. 68. 69. 70. 71. 72.

he made many innovative changes, thereby transforming the form and shape of the bicycle. Based on the context, the other choices are incorrect. a. This is the only choice that states an opinion. The writer cannot be certain that the safety bicycle would look familiar to today’s cyclists; it is his or her opinion that this is so. The other choices are presented as facts. b. To be apathetic is to show little emotion or interest; to be indifferent is to have no particular interest or concern. b. Surreptitious is acting in a stealthy or secretive manner. a. A deterrent prevents or discourages; encouragement inspires or heartens. d. Someone who is impertinent is rude; someone who is polite is courteous. d. To be animated is to be filled with activity or vigor; lively is to be filled with energy. c. To augment means to increase or expand in size or extent. c. To be ludicrous is to be absurd; to be reasonable is to be rational. b. Archaic means ancient or outdated; modern is current or contemporary. c. To be vindictive is to be vengeful; to be spiteful means to be malicious b. Jason or me is the object of the sentence; the objective pronoun me is used. d. In this sentence, the appositive—who ran in the Boston Marathon last year—describes Charlotte and is separated from the rest of

233

73.

74. 75.

76. 77.

78. 79. 80.

81. 82. 83. 84. 85. 86. 87. 88. 89. 90.

the sentence with commas. The word year’s is possessive and has an apostrophe. c. All proper nouns—Fourth of July and Morgan’s Beach—are capitalized correctly in this sentence. c. This sentence is in the past tense and uses the verb took. a. The subject of the sentence, art professor, is singular and takes the singular verb is planning. c. The subject forms should take the plural verb are, not the singular is. a. If completed, the sentence would read, Francine can run much faster than I can run; therefore, the subjective pronoun I should be used. b. The subject of the sentence one takes the singular verb was solved. c. Periods are correctly placed after all abbreviations in this sentence. c. This sentence has a comma before the conjunction but, which correctly connects the two complete thoughts in the sentence. d. aspirations a. compatible b. loquacious a. supervisor d. pneumonia d. no mistakes b. forfeit b. meteorology a. adjournment c. vengeance

C H A P T E R

16

Practice Test 2

235

––PRACTICE TEST 2––

5. 20% of what number equals 40% of 120? a. 48 b. 96 c. 200 d. 240

1. What is the mode of the following numbers? 12, 9, 8, 7, 7, 2, 9, 5, 7 a. 5 b. 7 c. 8 d. 9

6. The ratio of multimedia designers to graphic designers at a production house is 2:1. If the combined number of multimedia designers and graphic designers is 180, and half of the multimedia designers are women, how many women multimedia designers are there? a. 60 b. 80 c. 90 d. 120

Use the following chart to answer questions 2 and 3. METRIC UNITS TO ENGLISH UNITS CONVERSIONS

1 cm = .39 in. 1 m = 1.1 yd. 1 km = .6 mi.

2. 3.5 ft. is equivalent to approximately how many meters? a. 4 m b. 3.85 m c. 3.18 m d. 18 m

7. If a map drawn to scale shows 5.2 cm between two points and the scale is 1 cm = 1.5 km, how far apart are the two points in meters? a. 7.8 b. 780 c. 7,800 d. 78,000

3. 5 yd. 2 ft. is equivalent to approximately how many centimeters? a. 523 cm b. 79.56 cm c. 52.3 cm d. 6.63 cm

8. Use F = 95C + 32 to convert 113o F into the equivalent Celsius temperature. a. 38º b. 45º c. 54º d. 63º

4. Select the answer choice that best completes the sequence. VAB, WCD, XEF, , ZIJ a. AKL b. UHG c. YGH d. GHW

9. Damian earns a semimonthly salary of $2,300. What is his yearly salary? a. $55,200 b. $34,000 c. $27,600 d. $24,000

237

–PRACTICE TEST 2–

10. It took Amanda 45 minutes to jog 3 miles at a constant rate. Find her rate in mph. a. 3 mph b. 4 mph c. 10 mph d. 15 mph

15. What percent of 136 is 614 ? a. 5% b. 813% c. 33% d. 80 % Use the following information to answer questions 16–18.

11. What percent of a. 35 percent b. 30 percent c. 20 percent d. 25 percent

1  8

is

1 3 2?

1,200 new nursing students were asked to complete a survey in which they were asked which type of nursing they would like to pursue. The data was used to make the following pie chart. Nursing Survey

12. Nicole bought Blue Diamond stock at $15 per share. After six months, the stock is worth $20 per share. This represents a percent increase of a. 25%. b. 30%. c. 3313%. d. 75%. 13. One construction job can be completed by 15 workers in 8 days. How many days would if take 20 workers to complete the job? a. 4 days b. 6 days c. 8 days d. 10 days 14. 3 pieces of wood measure 8 yd. 2 ft. 1 in., 6 yd. 1 ft. 9 in., and 3 yd. 1 ft. 7 in. length. When these boards are laid end to end, what is their combined length? a. 18 yd. 17 in. b. 18 yd. 5 ft. c. 18 yd. 2 ft. 5 in. d. 18 yd. 5 in.

10% 30%

40%

Pediatrics Surgical Maternity ER

20%

16. How many nursing students would like to pursue pediatrics? a. 360 b. 400 c. 600 d. 800 17. Half of the nurses who indicated that would like to pursue surgical nursing also noted that they would like to transfer to a sister school across town. How many students indicated that they would like to make such a transfer? a. 240 students b. 120 students c. 60 students d. 10 students

238

––PRACTICE TEST 2––

18. If the same color scheme is used, which of the following bar graphs could represent the same data as the pie chart? a.

b.

21. Select the answer choice that best completes the sequence. B2CD, , BCD4, B5CD, BC6D a. B2C2D b. BC3D c. B2C3D d. BCD7 22. Select the answer choice that best completes the sequence.

c.

a. b. c. d.

d.

19. (85 × 34) ÷ (83 × 32) is equivalent to a. 576. b. 420. c. 376. d. 256. 20. Pipe A leads into a tank and Pipe B drains the tank. Pipe A can fill the entire tank in 1 hour. Pipe B can drain the entire tank in 45 minutes. At a certain point in time, the valves leading to both pipes are shut and the tank is 12 full. If both valves are opened simultaneously, how long will it take for the pipe to drain? a. 12 hr b. 1 hr c. 112 hr d. 134 hr

23. The reduced price of a computer is $1,250 after a 20% deduction is applied. The original price was a. $250. b. $1,000. c. $1,562.50. d. $6,250. 24. Three cylindrical solids with r = 7 m and h = 1 m are packed into a rectangular crate with l = 10 m, w = 9 m, and h = 1.2 m. The empty space will be filled with shredded paper. What volume will the shredded paper occupy? a. 86 m2 b. 66 m2 c. 42 m3 d. 42 m3

239

–PRACTICE TEST 2–

25. External hard drives cost $280 each. When more than 30 drives are purchased, a 10% discount is applied to each drive’s cost. How much money will 40 drives cost (excluding tax)? a. $7,000 b. $8,200 c. $10,080 d. $ 11,200

30. If the volume of a cube is 27 cubic centimeters, what is its surface area? a. 3 cm2 b. 6 cm2 c. 9 cm2 d. 54 cm2

26. Select the answer choice that best completes the following sequence. BOC, COB, DOE, EOD, a. FOG b. DOG c. DOF d. FOE

This graph shows the number of inches of rain for five towns in Suffolk County during spring 2007.

Use the following information to answer questions 31–33.

10 8 6 4 2 0

27. Which of the following is longest? (1 cm = 0.39 inches) a. 1 meter b. 1 yard c. 32 inches d. 85 centimeters

29. A box contains 23 iron washers, 15 steel washers, and 32 aluminum washers. If a washer is chosen at random, what is the probability that a steel washer will be chosen?

b. c. d.

3  14 23  70 32 7 0 15 7

Mastic Moriches Manorville Ridge

31. What was the median number of inches for the five towns? a. 5 b. 8 c. 9 d. 10

28. 25% = 1  a.  250 b. .4 c. 215 d. 04

a.

Shirley

32. What was the mode? a. 5 b. 8 c. 9 d. 10 33. What was the average number of inches for the season shown? a. 5 b. 8 c. 9 d. 10

240

––PRACTICE TEST 2––

34. When expressed as a percent, 197 is most accurately approximated as a. .0053%. b. 45.2 %. c. 50%. d. 52.9%.

39. Chris drove for 100 miles. During the first 45 miles, he drove at a rate of 75 mph. During the next 45 miles, he drove at a rate of 50 mph. For the last 10 miles, he drove at a rate of 25 mph. What was his approximate average rate for the whole trip? a. 40 mph b. 53 mph c. 55 mph d. 60 mph

35. The length of a rectangle is equal to 3 inches more than twice the width. If the width is 2 in., what is the area of the rectangle? a. 7 square inches b. 14 square inches c. 18 square inches d. 21 square inches

40. What is the area of the shaded figure inside the rectangle? 3

36. Kira’s register contains 10 20-dollar bills, 3 5-dollar bills, 98 1-dollar bills, 88 quarters, 52 dimes, 200 nickels, and 125 pennies. How much money is in the register? a. $351.45 b. $351.20 c. $350 d. $345.51 37. Select the answer choice that best completes the sequence. DEF, DEF2, DE2F2, , D2E2F3 a. DEF3 b. D3EF3 c. D2E3F d. D2E2 F2

12

3

Note: Figure not drawn to scale. a. 18 b. 36 c. 54 d. 60 Choose the correct vocabulary word for each of the following sentences. 41. Portland’s oldest citizen was

38. Hannah’s yard is square. A lamp is placed in the center of her yard. The lamp shines a radius of 10 feet on her yard, which is 20 feet on each side. How much of the yard, in square feet, is NOT lit by the lamp? a. 400 b. 40 – 10 c. 400 – 10 d. 400 – 100 241

; he refused to leave his home, even when he was warned of rising floodwaters. a. recitative b. redundant c. repatriated d. recalcitrant

–PRACTICE TEST 2–

42. Michael and Brenda had such terrific ; they always seemed to know, without being told, what the other felt. a. altercation b. equilibrium c. rapport d. symmetry 43. The politician’s voice detailed the many projects he planned to tackle once he was in office. a. clamorous b. flocculent c. affable d. fervent 44. The audience puzzled over the remark made by the mayoral candidate. a. obvious b. cryptic c. shrewd d. conniving 45. She shed heard the tragic news. a. copious b. scant c. nonchalant d. genteel

tears when she

46. After graduation, Charles requested a(n) so that he did not have to pay his school loans immediately. a. surrogate b. deferment c. tincture d. improvement

47. The nonprofit agency bought office supplies using a tax number. a. liability b. exempt c. information d. accountability 48. With this group of personalities, she was sure her party would be a success. a. scintillating b. mundane c. irradiated d. burnished 49. Her remarks were not taken seriously by anyone on the nominating committee. a. porous b. obsessive c. frivolous d. durable 50. A key reference book detailing eyewitness accounts had to have updates when new information surfaced. a. subsequent b. personable c. rote d. steadfast 51. The National Parks Service, in with its mission, preserves the great outdoors for all to enjoy. a. contention b. amnesty c. conflict d. accordance

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––PRACTICE TEST 2––

52. The exhibit at the botanical gardens is an unusual collection of cacti and other from around the world. a. perennials b. succulents c. annuals d. tubers 53. Although the freeway system continues to grow, it often cannot keep pace with a population. a. burgeoning b. beckoning c. capitulating d. exasperating 54. With admirable , the renowned orator spoke to the crowd gathered in the lecture hall. a. toil b. ado c. finesse d. tedium 55. The advice offered by his friend saved him from making a grave mistake. a. insensitive b. judicious c. metaphorical d. unorthodox Read the passage and respond to the questions that follow. Although many companies offer tuition reimbursement, most companies reimburse employees only for classes that are relevant to their position. This is a very limiting policy. A company that reimburses employees for all college credit courses—whether job-related or not—offers a service not only to the

243

employees, but to the entire company and greater community. One good reason for giving employees unconditional tuition reimbursement is that it shows the company’s dedication to its employees. In today’s economy, where job security is a thing of the past and employees feel more and more expendable, it is important for a company to demonstrate to its employees that it cares. The best way to do this is with concrete investments in the employees and their futures. In turn, this dedication to the betterment of company employees will create greater employee loyalty. A company that releases funds to pay for the education of its employees will get its money back by having employees stay with the company longer. Employee turnover will be reduced because even the employees who do not take advantage of the tuition reimbursement program will be more loyal to their company—just knowing that their company cares enough to pay for their education invokes loyalty. Most importantly, the company that has an unrestricted tuition reimbursement program will have higher quality employees. Although these companies do indeed run the risk of losing money on an employee who goes on to another job in a different company as soon as he or she gets a degree, more often than not, the employee will stay with the company. And even if employees do leave after graduation, it generally takes several years to complete any degree program. If the employee leaves upon graduation, the employer will have had a more sophisticated, more intelligent, and therefore more valuable and productive employee during that employee’s tenure with the company. If the employee stays, that education will doubly benefit the company. Not only is the employee more educated, but now that employee can be promoted, and the company does not have to fill a high-level

–PRACTICE TEST 2–

vacancy from the outside. Vacancies can be filled by people who already know the company well. Though unconditional tuition reimbursement requires a significant investment on the employer’s part, it is perhaps one of the wisest investments a company can make. 56. According to the passage, unconditional tuition reimbursement is good for which of the following reasons? a. Employees get a cheaper education. b. Employees become more valuable. c. Employees can find better jobs. d. Employers lose a great deal of money.

59. The writer most likely uses the word wisest in the last sentence, rather than words such as profitable, practical, or beneficial, because a. wisdom is associated with education, the subject of the passage. b. the writer is trying to appeal to people who are already highly educated. c. education could not be considered practical. d. the word beneficial is too abstract for readers to comprehend. 60. Which of the following words best describes the tone of this passage? a. insincere b. deceitful c. optimistic d. cynical

57. Which of the following statements from the passage is NOT an opinion? a. The best way to do this is with concrete investments in them. b. Most importantly, the company that has an unrestricted tuition reimbursement program will have higher quality employees. c. Although many companies offer tuition reimbursement, most companies only reimburse employees for classes that are relevant to their position. d. A company that puts out funds to pay for the education of its employees will get its money back by having employees stay with the company longer.

61. The passage suggests that, compared to employees of companies that offer unconditional tuition reimbursement, employees of companies that do not offer this benefit are a. less loyal. b. more likely to be promoted. c. not as smart. d. more likely to stay with the company.

58. The author’s reason for writing this passage was to a. entertain the reader. b. narrate a story. c. explain tuition reimbursement. d. persuade the reader.

62. In paragraph two, the word expendable most nearly means a. expensive. b. flexible. c. replaceable. d. extraneous.

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––PRACTICE TEST 2––

63. The main idea of the passage is that a. companies should reimburse employees for work-related courses. b. both companies and employees would benefit from unconditional tuition reimbursement. c. companies should require their employees to take college courses. d. by insisting on a college degree, companies will be better able to fill vacancies from within. Read each question and select the word that is the synonym or antonym for the word provided. 64. An antonym for disperse is a. gather. b. agree. c. praise. d. satisfy. 65. A synonym for droll is a. forget. b. charm. c. sedate. d. absurd. 66. A synonym for commendable is a. admirable. b. accountable. c. irresponsible. d. noticeable. 67. An antonym for prevarication is a. accolade. b. veracity. c. deprecation. d. mendacity.

68. An antonym for mirth is a. pallor. b. solemnity. c. penury. d. lethargy. 69. A synonym for domain is a. entrance. b. rebellion. c. formation. d. territory. 70. An antonym for orient is a. confuse. b. arouse. c. deter. d. simplify. Answer each of the following grammar and usage questions. 71. Which of the following sentences uses capitalization correctly? a. Last Thursday, my Mother, my Aunt Barbara, and I went to the museum to see an exhibit of African art. b. Last Thursday, my mother, my Aunt Barbara, and I went to the museum to see an exhibit of African art. c. Last Thursday, my mother, my aunt Barbara, and I went to the Museum to see an exhibit of African art. d. Last Thursday, my mother, my aunt Barbara, and I went to the museum to see an exhibit of African Art.

245

–PRACTICE TEST 2–

72. Which of the following sentences uses periods correctly? a. Dr Harrison will speak at the hotel in Chicago, Ill, on thurs at 3:00 P.M. b. Dr. Harrison will speak at the hotel in Chicago, Ill, on Thurs at 3:00 P.M. c. Dr Harrison will speak at the hotel in Chicago, Ill, on Thurs. at 3:00 P.M. d. Dr. Harrison will speak at the hotel in Chicago, Ill., on Thurs. at 3:00 P.M.

75. Which of the following sentences uses the correct verb form? a. Margaret brang a cake so that everyone in the office could help celebrate her birthday. b. Margaret brought a cake so that everyone in the office could help celebrate her birthday. c. Margaret bring a cake so that everyone in the office could help celebrate her birthday. d. Margaret had brung a cake so that everyone in the office could help celebrate her birthday.

73. Which of the following sentences is NOT a complete sentence? a. Hearing the thunder, the lifeguard ordered us out of the water. b. Turn off the lights. c. Sunday afternoon spent reading and playing computer games. d. I was surprised to see that my neighbor had written a letter to the editor.

76. Which of the following sentences shows subject/verb agreement? a. Neither of the dogs have been to obedience training. b. Neither of the dogs were to obedience training. c. Neither of the dogs is been to obedience training. d. Neither of the dogs has been to obedience training.

74. Which of the following sentences is a complete sentence? a. The newspapers are supposed to be delivered by 7:00, but I am usually finished before 6:45. b. I called the delivery service this morning, they told me the shipment would arrive on time. c. Look in the closet you should find it there. d. I was the first to sign the petition Harry was the second.

77. Which of the following sentences shows subject/verb agreement? a. One of the customers have complained about poor service. b. Neither of the customers have complained about poor service. c. Each of the customers have complained about poor service. d. Some of the customers have complained about poor service.

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––PRACTICE TEST 2––

78. Which of the following sentences does NOT use the italicized pronoun correctly? a. Alicia and me want to spend Saturday at Six Flags Amusement Park. b. Either Sam or William will bring his CD player to the party. c. She and I will work together on the project. d. Why won’t you let her come with us? 79. Which of the following sentences uses the italicised pronouns correctly? a. Four band members and me were chosen to attend the state competition; one of you will do the driving. b. Four band members and me were chosen to attend the state competition; one of us will do the driving. c. Four band members and I were chosen to attend the state competition; one of we will do the driving. d. Four band members and I were chosen to attend the state competition; one of us will do the driving. Choose the misspelled word in the following questions. If there are no mistakes, select choice d. 80. a. b. c. d.

embarrassment accomodate weird no mistakes

81. a. inadvertant b. occasion c. liquefy d. no mistakes

82. a. b. c. d.

tyranny dessicate subpena no mistakes

83. a. b. c. d.

dictionary auditorium biology no mistakes

84. a. b. c. d.

geometry perimeter circumferance no mistakes

85. a. b. c. d.

general corporal lieutenant no mistakes

Choose the correct spelling of the word for the following sentences. 86. Do you think I should run for a seat on the city ? a. counsel b. council 87. The amount for the carpet was a price. a. fair b. fare 88. This problem is a. two b. to c. too

247

complex.

–PRACTICE TEST 2–

89. My grandmother is an historian. a. imminent b. immanent c. eminent

90.

only four o’clock in the afternoon. a. It’s b. Its

248

–PRACTICE TEST 2–



Answers

1. b. To find the mode, see which number occurs the most: 12, 9, 8, 7, 7, 2, 9, 5, 7. Thus, 7 is the mode. 2. c. You should know that 3 ft. = 1 yd. and the chart tells you that 1 m = 1.1 yd. Thus, you can create conversion factors that let you cross off feet and end up with meters: 3.5 ft. × 1m 1 yd.  ×  1.1  yd. ≈ 3.18 m. 3 ft. 3. a. 5 yd. = 15 ft., so 5 yd. 2 ft. = 17 ft. Next, using the fact that 1 ft. = 12 in. and 1 cm = .39 in., you can create conversion factors that let you cross off feet and end up with 1 cm 12 i n.   cm: 17 ft. ×  1 ft. × .39 in. ≈ 523 cm. 4. c. The first term of each triplet represents the alphabet in sequence: V  W  X  Y  Z. Thus, the first letter of the missing triplet is Y. The second and third letters of the triplets follow the pattern of skipping one letter. Thus, the second term of the missing triplet will be: A  C  E  G  I. And the third term of the missing triplet will be: B  D  F  H  I. Therefore, the answer is YGH. 5. d. “20% of what number equals 40% of 120?” can be written mathematically as .20 × x = .40 × 120. Dividing both sides by .20 yields: (.40)(120) x= = 240 .2 0 6. a. You are told that the ratio of multimedia designers to graphic designers at a production house is 2:1. Thus, 23 of the 180 total must be multimedia designers. 23 of 180 = 23  180 = 120 multimedia designers. Half of these are women, so there are 60 women multimedia designers. 7. c. First use a proportion to get the real-life 5.2 cm 1 cm value:  1.5  km =  x k m ; x = 1.5 × 5.2 = 7.8 km. Next, convert kilometers to meters by multi1,000 m 1,000 m plying by  1 k m : 7.8 km ×  1 k m = 7,800 m.

249

8. b. Substitute 113 for F in the given equation. Thus, F = 95 C + 32 becomes 113 = 95 C + 32; 113 – 32 = 95 C; 81 = 95 C; 81 × 59 = C; 9 × 5 = C; C = 45 degrees. 9. a. Recall that semimonthly means twice a month. This means he makes 2 × $2,300 = $4,600 per month. Multiply by 12 months per year: 12 months × $4,600 = $55,200 per year. 10. b. First, you should rearrange D = RT into R = D . Substitute the given values into the forT mula. Here, R = 45 min = 34 hour, and D = 3 mi. Thus, R = DT becomes R = 3 mi ÷ 34 hr = 4 mph. 11. d. The question “What percent of 18 is 312 ?” can x 1 1 be written mathematically as  10 0 × 8 = 3 2. x Recall that what percent is  10 0 , of means ×, x 1 and is means =. Solving, you get  80 0 = 3 2; x = 800  = 25%. 32 12. c. The Blue Diamond stock rose from $15 to $20. This is a difference of $20 – $15 = $5. When compared with the original $15, 155 = x 500 1   10 0 ; x = 1 5 = 33 3 %. 13. b. If it takes 15 workers 8 days to complete a job, it would take 1 worker 15 × 8 = 120 days. It would take 20 workers 120 ÷ 20 = 6 days. 14. c. First, line up and add all of the units: 8 yd. 2 ft. 1 in. 6 yd. 1 ft. 9 in. + 3 yd. 1 ft. 7 in. 17 yd. 4 ft. 17 in. Next, note that 12 in. = 1 ft., so 17 yd. 4 ft. 17 in. is the same as 17 yd. 5 ft. 5 in. Next, note that 3 ft. = 1 yd., so you can rewrite the length as 18 yd. 2 ft. 5 in. 15. b. Recall that “What percent” can be expressed x 3 as  10 0 . The question “What percent of 1 6 is

–PRACTICE TEST 2–

1 x 3 6 4 ?” can be expressed as:  10 0 × 1 6 = 614 ; 3 × x = 25; x = 235 = 813%.

=

1 3×x 6  4;  1,600

16. a. 30% (black sector) of the 1,200 nursing stu dents indicated that they would like to pursue pediatrics; .30 × 1,200 = 360 students. 17. b. 20% (darkest gray) of the nursing students chose surgical nursing. Half of these want to transfer to the sister school, so that is 10%. 10% of 1,200 = .10 × 1,200 = 120 students. 18. b. If the same color scheme is used (as stated), then in decreasing size order, the bars should be lightest gray, black, darkest gray, and medium gray. Only choice b has bars that match this description. 19. a. You can apply the rules of exponents to the terms that have the same bases. Thus, (85 × 34) ÷ (83 × 32) is equivalent to 85 – 3 × 34 – 2 = 82 × 32 = 64 × 9 = 576. Recall that when multiplying and/or dividing exponential numbers, those exponents of numbers with the same base value (e.g., 85, 83, or 34, 32) can be either added or subtracted depending on the operation asked to be performed (multiplication → add exponents, division → subtract exponents). 20. c. First, convert the hour into minutes. 1 hour = 60, so Pipe A fills 610 of the tank every minute. Pipe B empties 415 of the tank per minute. This means the net effect—every minute—is 1 1 4 3 1 4 – =  of the tank is 5 – 6 0 = 180 180 180 1 drained. If 2 of the tank is initially full, this 90 equals  18 0 full. It will take 90 minutes for the 90 1   per minute). 18 0 to drain out (at a rate of  180 1 90 min = 12 hr. 21. b. Notice that the number grows by 1 and moves to the letter on the right of its current position: B2CD, BC3D, BCD4, B5CD, BC6D. Thus, the missing term is BC3D.

250

22. d. Note that the number of line segments increases and then decreases by one: 1  2  3  4  5  4  3. Thus the next 2 members of the series will have 2 sides and then 1 side. 23. c. If a 20% deduction was applied, then $1,250 represents 80% of the original cost. This question is really asking: “80% of what is $1,250?” This can be written mathematically 1,250  as .80 × x = 1,250; x =  .80 = $1,562.50. 24. d. The formula for a cylinder is V = r 2h. If you use  ≈ 272 , and substitute the given values into this formula, you have: V = 272 × (7)2 × 1 = 272 × 7 = 22 m3. Three such cylinders will occupy a volume of 3 × 22 m3 = 66 m3 inside the rectangular crate. The volume of the crate is lwh = 10 × 9 × 1.2 = 108 m3. The empty space (to be filled with shredded paper) is 108 m3 – 66 m3 = 42 m3. 25. c. Since more than 40 drives are being purchased, use the discounted price. Take 10% ($28) off the cost of each drive. So, instead of costing $280 each, the drives will cost $280 – $28 = $252 each. Next, multiply 40 drives by the price of each drive: 40 × 252 = $10,080. 26. a. The first term progresses from B  C  D  E, so the last triplet will begin with F. Note that the second term is always O. Every other triplet is the inverse of the triplet before it. So, the third letter of the last triplet, like its predecessors, is the next letter of the alphabet after F. 27. a. In order to compare the choices, covert them all into inches: 39 in. a. 1 m = 100 cm = 100 cm ×  cm = 39 in. b. 1 yd. = 36 in. c. 32 in. d. 85 cm is less than 1 m (choice a) so you need not waste time converting this choice to inches. Thus, choice a, 1 m (39 inches) is the longest.

––PRACTICE TEST 2––

28. a. This can be solved by equating the percent to its equivalent fractional form(s): 25% = .4% = 4 1 . .004 =  1,0 00 =  250 29. a. First, add all the washers together: 23 + 15 + 32 = 70. There are 15 steel washers, so the chance of pulling a steel washer is 15 out of 70: 1750 = 134 . 30. d. The volume formula for a cube is V = s 3, so here s 3 = 27 and s = 3 cm. The surface area of one face is s2 = 32 = 9 cm2. Since there are six faces, the total surface area is 6 × 9 cm2 = 54 cm2. 31. d. First, list the numbers in order. The middle number will be the median: 5 5 10 10 10 32. d. To find the mode, select the number that occurs the most: 10 10 5 5 10 10 occurs three times and is the mode. 33. b. First, add up all the values: 10 + 10 + 5 + 5 + 10 = 40. Next divide by 5 (the number of values): 40 ÷ 5 = 8 inches. 34. d. First, convert 197 to a decimal: 9 ÷ 17 ≈ .529. Next, to express this value as a percent, move the decimal point over two places to the right ≈ 52.9%. 35. b. “The length of a rectangle is equal to 3 inches more than twice the width,” can be expressed mathematically as l = 2w + 3. You know w = 2, so l = (2)(2) + 3 = 7. The area is then A = lw = 7 × 2 = 14 square inches. 36. a. First, multiply the number of coins (or bills) by the value of the coin (or bill): 10 20-dollar bills = 10 × $20 = $200 3 five-dollar bills = 3 × $5 = $15 98 one-dollar bills = 98 × $1 = $98 88 quarters = 88 × $.25 = $22 52 dimes = 52 × $.10 = $5.20 200 nickels = 200 × $.05 = $10 125 pennies = 125 × $.01 = $1.25

251

Next, add up all the money: $200 + $15 + $98 + $22 + $5.20 + $10 + $1.25 = $351.45. 37. d. The letters remain the same: DEF. The numbers change as follows (a dash, such as “-“ represents no number): - - -  - - 2  - 2 2  2 2 2  2 2 3. 38. d. The area of the dark yard is the area of her square yard (A = s2) minus the circle of light around the lamp (A = r 2).

20 ft.

Thus, the dark area = 202 – ( × 102), or 400 – 100. 39. b. To find the average rate, you must use D = RT with the total distance and the total time as D and T respectively. You are given the total distance of 100 miles. You need the total time. This can be found by using the information in the question. The formula D = RT can be rewritten as T = DR. Making a chart for yourself will help you stay organized: INFO

TIME

45 mi @ 75 mph

90 45    T = D R = 75 = 150 hr

45 mi @ 50 mph

45 135    T = D R = 50 = 150 hr

10 mi @ 25 mph

60 10    T = D R = 25 = 150 hr

*Note that the least common multiple of 75, 50, and 25 was chosen as the denominator for the times listed. 285  Total time =  150 hr = 1.9 hr

–PRACTICE TEST 2–

40.

41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52.

Now you can use the total time and total distance in the formula D = RT. Since you want R, you can rearrange this formula to R = D ÷ T. Thus, you have R = D ÷ T = 100 ÷ 1.9 ≈ 53 mph. c. Each little white triangle in the corner is a tiny right triangle with a hypotenuse of 18  2 2 2 and a leg of 3. Use a + b = c to find the other leg: 32 + b2 =(18 )2; 9 + b2 = 18; b2 = 9; b = 3. Thus the width of the rectangle is 3 + 3 = 6 units. The area of the entire rectangle is lw = 12 × 6 = 72 units2. To find the area of the shaded region, you must subtract out the area of the 4 tiny triangles. Each triangle has an area equal to 12bh = 12 × 3 × 3 = 4.5 units2, so the four triangles take up 4 × 4.5 = 18 units2. Subtract this amount from the area of the rectangle to find the area of the shaded region: 72 – 18 = 54 units2. d. To be recalcitrant is to be stubbornly resistant. c. To have rapport is to have mutual trust and emotional affinity. d. A fervent voice is one that has great emotion or zest. b. Cryptic means mysterious, hidden, or enigmatic. a. Copious means plentiful or abundant. b. A deferment is a delay. b. Exempt means to be excused from a rule or obligation. a. That which is scintillating is brilliant or sparkling. c. Frivolous means not worthy of serious attention; of little importance. a. Subsequent means following a specified thing in order or succession. d. Accordance means in agreement or harmony. b. Succulents are plants that have leaves specifically for storing water.

252

53. a. Burgeoning means emerging or new growth. 54. c. Finesse is skill, tact, and cleverness. 55. b. Judicious means to use or show good judgment; to be wise or sensible. 56. b. The idea that employees will become more valuable if they take courses is stated in the fourth paragraph: “the employer will have had a more sophisticated, more intelligent, and therefore more valuable and productive employee.” 57. c. This statement describes the many positions that companies can take when considering reimbursement for educational classes. This statement could be verified as fact by surveying companies to find out their tuition reimbursement policies. 58. d. The writer of this passage states an opinion: “A company that reimburses employees for all college credit courses—whether job related or not—offers a service not only to the employees but to the entire company.” The writer then proceeds to give reasons to persuade the reader of the validity of this statement. 59. a. By using a word associated with education, the writer is able to reinforce the importance of education and tuition reimbursement. 60. c. The passage is optimistic and describes only positive effects of unconditional reimbursement; there are virtually no negative words. 61. a. If employees of companies that offer unconditional tuition reimbursement are more loyal to their companies (see the second and third paragraphs), it follows that other employees will be less loyal because their company is not showing enough dedication to their betterment. 62. c. Expendable means replaceable. The writer uses the word immediately after saying that

––PRACTICE TEST 2––

63.

64. 65. 66. 67. 68. 69.

70. 71. 72. 73.

job security is a thing of the past. This clue tells you that workers do not feel they are important or valuable to a company that can fire them on a moment’s notice. b. This main idea is explicitly stated in the last sentence of the first paragraph and again at the end of the passage. a. Disperse means to scatter; to gather means to collect in one place. c. Droll means to have a humorous or odd quality; sedate means unruffled or serious. a. Both commendable and admirable mean worthy, qualified, or desirable. b. Prevarication is an evasion of the truth; veracity means truthfulness. b. Mirth means merriment; solemnity means seriousness. d. A domain is an area governed by a ruler; a territory is an area for which someone is responsible. a. To orient means to adjust, become familiar; to confuse means to bewilder. b. Every proper noun and adjective in this sentence is correctly capitalized. d. Periods are placed after Dr., Ill., Thurs., and P.M. c. This is a sentence fragment and is missing the helping verb was that would make it a complete sentence.

253

74. a. Choice a is the only complete sentence. Choices b, c, and d are run-on sentences. 75. b. This sentence is in the past tense and correctly uses the verb brought. 76. d. Neither is singular, as is has been. 77. d. Some is plural, as is have complained. 78. a. Alicia and I is the subject of the sentence; therefore, the subjective pronoun I has to be used to make the sentence correct. 79. d. Four band members and I is the subject of the sentence; the subjective pronoun I is correct. Us is the object of the preposition; the objective pronoun us is correct. 80. b. accomodate 81. a. inadvertent 82. c. subpoena 83. d. no mistakes 84. c. circumference 85. d. no mistakes 86. b. council 87. a. fair 88. c. too 89. c. eminent 90. a. It’s

S E C T I O N

Helpful Resources

5 T

his book has provided you with focused practice and an essential review of math and vocabulary skills. Now, use these additional helpful resources to drive home some key skills before you sit down to take the civil service exam. In the math and vocabulary glossaries as well as the commonly tested words appendix, you will find a compiled list of terms you may need to know for the civil service exam. These lists can seem intimidating, but don’t let that prevent you from tackling them. If the word list looks intimidating, try this: 1. Figure out how many days there are until you take the civil service exam. 2. Multiply that number by 10. If you have 30 days until the test day, you can learn 300 new words by learning only ten new words each day! And, remember, some of these words may already be familiar to you. Each night, target ten words that you feel you do not know. Read the definitions and the way each word is used in a sentence. Try to use the words in conversation, in your reports or memos, or even in an e-mail. The more you use a word, the more familiar it will become to you. When words are familiar, you can count on them to help you with all forms of communication—or to pass any kind of test. One way to manage these word lists is to work with flash cards. Write the vocabulary word on one side and the definition on the other. Or, try writing a sentence that uses the word on one side of the flash card and the definition of the word on the other. Flash cards are easy to handle and they’re portable. In this resource section, you will also find a list of some of the most common Latin and Greek word roots, prefixes, and suffixes. A familiarity with common prefixes, suffixes, and word roots can dramatically improve your ability to determine the 255

–MATH AND VOCABULARY FOR CIVIL SER VICE TESTS–

meaning of unfamiliar vocabulary words. The tables list common prefixes, suffixes, and word roots; their meanings; an example of a word with that prefix, suffix, or word root; the meaning of that word; and a sentence that demonstrates the meaning of that word. Review the list carefully, taking note of the examples, which are mostly everyday words. Remember to study any roots, prefixes, or suffixes that are unfamiliar to you.

In this section, you will also find a quick math reference sheet with many of the formulas you will need to know for math questions on the civil service exam. These resources are here to make your math and vocabulary skills stronger before the day of your civil service exam—make the commitment to work with them as you prepare for your exam.

256

Appendix 1: Glossary of Math Terms

area: a measure of the space inside a two-dimensional figure. Area is expressed in square units. arithmetic series: a series that progresses by adding (or subtracting) a constant number to each term. associative law: this property applies to grouping of addition or multiplication equations and expressions. It can be represented as a + (b + c) = (a + b) + c or a × (b × c) = (a × b) × c. For example, 10 + (12 + 14) = (10 + 12) + 14. circumference: the distance around a circle. commutative law: this property applies to addition and multiplication and can be represented as a + b = b + a or a × b = b × a. For example, 2 + 3 = 3 + 2 and 4 × 2 = 2 × 4 exhibit the commutative law. compounded annually: interest is paid each year. compounded daily: interest is paid every day. compounded monthly: interest is paid every month. compounded quarterly: interest is paid four times per year. compounded semiannually: interest is paid two times per year. constant rate equation: an equation that is used to relate distance, rate, and time when dealing with a constant velocity: D = RT. denominator: the bottom number in a fraction. diameter: any line segment that goes through the center of a circle and has both endpoints on the circle. difference: the answer obtained by subtracting. distributive law: this property applies to multiplication over addition and can be represented as a(b + c) = ab + ac. For example, 3(5 + 7) = 3 × 5 + 3 × 7. geometric series: a series that progresses by multiplying each term by a constant number to get the next term. improper fraction: a fraction whose numerator is greater than the denominator, such as 78.

257

–APPENDIX 1: GLOSSARY OF MATH TERMS–

least common denominator (LCD): the smallest number that is a multiple of the original denominators present. mean: the average of a set of values found by adding the values and dividing by the number of values. median: the middle number in a group of numbers arranged in sequential order. In a set of numbers, half will be greater than the median and half will be less than the median. mixed number: A number that is expressed as a whole number with a fraction to the right, such as 121. mode: the number in a set of numbers that occurs most frequently. To find the mode, look for numbers that occur more than once and find the one that appears most often. numerator: the top number in a fraction. order of operations: The order in which operations must be performed. An easy way to remember the order of operations is to use the mnemonic PEMDAS, where each letter stands for an operation: Parentheses: Always calculate the values inside of parentheses first; Exponents: Second, calculate exponents (or powers); Multiplication/Division: Third, multiply or divide in order from left to right; Addition/Subtraction: Last, add or subtract in order from left to right. percent change: when calculating the percent increase or decrease, equate the ratio of the amount of change to the initial value with the ratio of a new value, x, to 100. The general prox c ha ng e   portion to use is:  initial = 100 percent error: found by converting the ratio between the calculated value and the actual value to a difference in values x value out of 100:  = actual values 10 0

percent: a ratio that expresses a value as per 100 parts. For example, 30% is equivalent to 30 per 30 100, or  10 0 . You can express a percent as a fraction by placing the number before the percent symbol over the number 100. You can express a percent as a decimal by moving the current decimal point two places to the left. perimeter: the distance around a two-dimensional geometric figure. prime number: a number that has only two factors, the number 1 and itself. product: the answer obtained by multiplying. proper fraction: a fraction where the numerator is less than the denominator, such as 21. proportion: a pair of equivalent ratios in the form ba = cd quotient: the answer obtained by dividing. radius: any line that begins at the center of a circle and ends on a point on the circle. ratio: a comparison of two or more numbers. reciprocal: the multiplicative inverse of a number; for example, the reciprocal of 54 is 45. simple interest: interest is calculated with the formula I = PRT. The amount of money deposited is called the principal, P. The annual interest rate is represented by R, and T represents the time in years. sum: the answer obtained by adding. symbol series: a visual series based on the relationship between images. volume: a measure of the amount of space inside a three-dimensional shape. Volume is expressed in cubic units.

258

Appendix 2: Math Formula Sheet

Percent part percent  =   whole 10 0

is  of

=

percent  10 0

change  original

=

percent  10 0

Perimeter Rectangle: P = 2 × l + 2 × w

Distance Formula D=R×T

Circumference: C =  × d or C = 2 ×  × r

Simple Interest Formula I=P×R×T

Area Triangle: A = 12 × b × h Rectangle: A = b × h Trapezoid: A = 12 × h × (b1 + b2)

Rules of Exponents x0 = 1 x–a = x1a xa × xb = xa + b xa xb = xa – b (xa)b = xa × b

xa ÷ xb = xa – b a  x= x 1 a

Probability #favorable outcomes P(E) =  P(E1 or E2) = P(E1) + P(E2) #total outcomes P(E1 and E2) = P(E1) × P(E2)

Square: P = 4 × s

Volume V = B × h (B is the area of the base) Rectangular Solid: V = l × w × h Cylinder: V =  × r2 × h

Pythagorean theorem: a2 + b2 = c2

259

Appendix 3: Glossary of Vocabulary Terms active voice: when the subject is performing the action (as opposed to passive voice). agreement: the state of being balanced in number (e.g., singular subjects and singular verbs; plural antecedents and plural pronouns). antecedent: the noun that is replaced by a pronoun. cause: a person or thing that makes something happen. clause: a group of words containing a subject and predicate. comparative: the adjective form showing the greater degree in quality or quantity, formed by adding -er (e.g., happier). comparison: showing how two ideas or items are similar. complex sentence: a sentence with at least one dependent and one independent clause. compound sentence: a sentence with at least two independent clauses. conjunctive adverb: a word or phrase that often works with a semicolon to connect two independent clauses and show the relationship to one another (e.g., however, therefore, likewise). contraction: a word that uses an apostrophe to show that a letter or letters have been omitted (e.g., can’t). contrast: showing how two ideas or items are different. coordinating conjunction: one of seven words—and, but, for, nor, or, so, yet—that serve to connect two independent clauses. dependent clause: a clause that has a subordinating conjunction and expresses an incomplete thought. direct object: the person or thing that receives the action of the sentence. fragment: an incomplete sentence (may or may not have a subject and predicate). gerund: the noun form of a verb, created by adding -ing to the verb base.

261

–APPENDIX 3: GLOSSARY OF VOCABULARY TERMS–

helping verb: (auxiliary verb) verbs that help indicate exactly when an action will take place, is taking place, did take place, should take place, might take place, etc. homophone: a word that sounds exactly like another word but has a different spelling and meaning (e.g., bare, bear). independent clause: a clause that expresses a complete thought and can stand on its own. indirect object: the person or thing that receives the direct object. infinitive: the base form of a verb plus the word to (e.g., to go). intransitive verb: a verb that does not take an object (the subject performs the action on his/her/itself). mechanics: the rules governing punctuation, capitalization, and spelling. modifier: a word or phrase that describes or qualifies a person, place, thing, or action. parallel structure: a series of words, phrases, or clauses that all follow the same grammatical pattern. participial phrase: the adjective form of a verb, created by adding -ing to the verb base. passive voice: when the subject of the sentence is being acted upon (passively receives the action). past participle: the verb form expressing what happened in the past, formed by a past tense helping verb + the simple past tense form of the verb. phrase: a group of words that do not contain both a subject and a predicate. predicate: the part of the sentence that tells us what the subject is or does. present participle: the verb form expressing what is

happening now, formed by a present tense helping verb and -ing. proper noun: a noun that identifies a specific person, place, or thing, such as Elm Street. redundancy: the unnecessary repetition of words or ideas. run-on: a sentence that has two or more independent clauses without the proper punctuation or connecting words (e.g., subordinating conjunction) between them. style: the manner in which something is done; in writing, the combination of a writer’s word choice, sentence structure, tone, level of formality, and level of detail. subject: the person, place, or thing that performs the action of the sentence. subjunctive: the verb form that indicates something that is wished for or contrary to fact. subordinating conjunction: a word or phrase that introduces an adverb clause, making the clause dependent and showing its relationship to another (usually independent) clause (e.g., because, since, while). superlative: the adjective form showing the greatest degree in quality or quantity, formed by adding -est (e.g., happiest). transition: a word or phrase used to move from one idea to the next and to show the relationship between those ideas (e.g., however, next, in contrast). transitive verb: a verb that takes an object (someone or something receives the action of the verb). usage: the rules that govern the form of the words you use and how you string words together in sentences.

262

Appendix 4: Commonly Tested Vocabulary Words aberration (a˘b·e˘·'ray·sho ˘n) n. deviation from what is

abstain (ab·'stayn) v. to choose to refrain from some-

normal, distortion. His new scientific theory was

thing, especially to refrain from voting. I have decided

deemed an aberration by his very conservative

to abstain on this issue.

colleagues.

abstruse (ab·'stroos) adj. difficult to comprehend,

abeyance (a ˘·'bay·a ˘ns) n. suspension, being temporarily

obscure. Albert Einstein’s abstruse calculations can be

suspended or set aside. Construction of the highway is in

understood by only a few people. abysmal (a ˘·'biz·ma ˘l) adj. 1. extreme, very profound, limit-

abeyance until we get agency approval. abhor (ab·'hohr) v. to regard with horror, detest. I abhor

less 2. extremely bad. Tom’s last-place finish in the race

such hypocrisy!

was an abysmal turn of events for the team. accolade ('ak·o ˘·layd) n. 1. praise or approval 2. a cere-

abjure (ab·'joor) v. 1. to repudiate, renounce under oath 2. to give up or reject. When Joseph became a citizen,

monial embrace in greeting 3. a ceremonious tap on

he had to abjure his allegiance to his country of origin.

the shoulder with a sword to mark the conferring of

abrogate ('ab·ro ˘·ayt) v. to abolish, do away with, or

knighthood. He received accolades from his superiors

annul by authority. It was unclear if the judge would

for finding ways to cut costs and increase productivity. accretion (a˘·'kree·sho ˘n) n. 1. growth or increase by

abrogate the lower court’s ruling. abscond (ab·'skond) v. to run away secretly and hide, often

gradual, successive addition; building up 2. (in biol-

in order to avoid arrest or prosecution. Criminals will

ogy) the growing together of parts that are normally

often head south and abscond with stolen goods to Mexico.

separate. The accretion of sediment in the harbor chan-

absolution (ab·so ˘·'loo·sho ˘n) n. 1. an absolving or clearing from blame or guilt 2. a formal declaration of for-

nel caused boats to run aground. acrid ('ak·rid) adj. 1. having an unpleasantly bitter, sharp

giveness, redemption. The jury granted Alan the

taste or smell 2. bitter or caustic in language or manner.

absolution he deserved.

The burning tires in the junkyard gave off an acrid odor.

263

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

anachronism (a ˘·'nak·ro ˘·niz·e˘m) n. 1. something that is

ad hoc (ad 'hok) adj. for a specific, often temporary, purpose; for this case only. She acted as the ad hoc scout

placed into an incorrect historical period 2. a person,

leader while Mr. Davis—the official leader—was ill.

custom, or idea that is out of date. The authenticity and

adamant ('ad·a˘·ma˘nt) adj. 1. unyielding to requests,

credibility of the 1920s movie were damaged by the many

appeals, or reason 2. firm, inflexible. The senator was

anachronisms that appeared throughout the scenes.

adamant that no changes would be made to the defense

anarchy ('an·a˘r·kee) n. 1. the complete absence of gov-

budget.

ernment or control resulting in lawlessness 2. political

addle ('ad·e˘l) v. 1. to muddle or confuse 2. to become rot-

disorder and confusion. The days immediately follow-

ten, as in an egg. The jury found the defendant addled

ing the revolution were marked by anarchy. anomaly (a˘·'nom·a˘·lee) n. something that deviates from

at the end of the prosecuting attorney’s questions. ado (a˘·'doo) n. fuss, trouble, bother. Without much ado,

the general rule or usual form; one that is irregular,

she completed her book report.

peculiar or abnormal. Winning millions of dollars from

aficionado (a˘·'fish·yo·'nah·doh) n. a fan or devotee,

a slot machine would be considered an anomaly. antipathy (an·'tip·a˘·thee) n. 1. a strong aversion or dis-

especially of a sport or pastime. The Jeffersons’ attendance at every game proved that they were true afi-

like 2. an object of aversion. It is a moment I recall

cionados of baseball.

with great antipathy.

alacrity (a˘·'lak·ri·tee) n. a cheerful willingness; being

antithesis (an·'tith·e˘·sis) n. the direct or exact opposite,

happily ready and eager. The alacrity she brought to

opposition or contrast. Martin’s parenting style is the

her job helped her move up the corporate ladder quickly.

antithesis of mine.

allay (a˘·'lay) v. 1. to reduce the intensity of, alleviate 2. to

apathetic (ap·a˘·'thet·ik) adj. feeling or showing a lack of

calm, put to rest. The remarks by the C.E.O did not

interest, concern, or emotion; indifferent, unrespon-

allay the concerns of the employees.

sive. Ms. Brownstone was distressed by how apathetic

altercation (awl·te˘r·'kay·sho ˘n) n. a heated dispute or

her eighth-grade students were. aperture ('ap·e˘r·chu ˘r) n. an opening or gap, especially

quarrel. To prevent an altercation at social functions, one should avoid discussing politics and religion.

one that lets in light. The aperture setting on a camera

ambivalent (am·'biv·a˘·le˘nt) adj. having mixed or con-

has to be set perfectly to ensure that pictures will have

flicting feelings about a person, thing, or situation;

enough light.

uncertain. She was ambivalent about the proposal for

apex ('ay·peks) n. 1. the highest point 2. tip, pointed end.

the shopping center because she understood the argu-

Upon reaching the apex of the mountain, the climbers

ments both for and against its construction.

placed their flag in the snow.

ameliorate (a˘·'meel·yo ˘·rayt) v. to make or become bet-

apocalypse (a˘·'pok·a˘·lips) n. a cataclysmic event bring-

ter, to improve. The diplomat was able to ameliorate

ing about total devastation or the end of the world.

the tense situation between the two nations.

Many people feared an apocalypse would immediately

amorphous (a˘·'mor·fu ˘s) adj. having no definite shape or form; shapeless. The amorphous cloud of steam drifted

follow the development of nuclear weapons. apostate (a˘·'pos·tayt) n. one who abandons long-held

over her head.

religious or political convictions. Disillusioned with

amulet ('am·yu ˘·lit) n. something worn around the neck

the religious life, Reverend Gift lost his faith and left

as a charm against evil. The princess wore an amulet

the ministry, not caring if he’d be seen as an apostate by

after being cursed by a wizard.

colleagues who chose to remain.

264

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

apotheosis (a˘·poth·ee·'oh·sis) n. deification, an exalted

through the Arctic has become the subject of many books

or glorified ideal. Lancelot was the apotheosis of

and movies. ascetic (a˘·'set·ik) adj. practicing self-denial, not allowing

chivalry until he met Guinevere. appease (a˘·'peez) v. to make calm or quiet, soothe; to still

oneself pleasures or luxuries; austere. Some religions

or pacify. His ability to appease his constituents helped

require their leaders to lead an ascetic lifestyle as an

him win the election.

example to their followers.

apprise (a˘·'pr¯z) v. to inform, give notice to. Part of

askew (a˘·'skyoo) adj. & adv. crooked, not straight or

Susan’s job as a public defender was to apprise people of

level; to one side. Even the pictures on the wall stood

their legal rights.

askew after my five-year-old son’s birthday party.

approbation (ap·ro ˘·'bay·sho ˘n) n. approval. The local

asperity ('a˘·sper·i·tee) n. harshness, severity; roughness

authorities issued an approbation to close the street for a

of manner, ill temper, irritability. The asperity that

festival on St. Patrick’s Day.

Marvin, the grumpy accountant, brought to the meet-

appropriate (a ˘·'pro¯ ·pre¯·˘t) v. to take for one’s own use, often without permission; to set aside for a special

ings usually resulted in an early adjournment. assay ('a˘·say) v. 1. to try, put to a test 2. to examine 3. to

purpose. The state legislature will appropriate two mil-

judge critically, evaluate after an analysis. The chief

lion dollars from the annual budget to build a new

engineer wanted a laboratory to assay the steel before

bridge on the interstate highway.

using it in the construction project.

apropos (ap·ro ˘·'poh) adj. appropriate to the situation;

assiduous (a˘·'sij·oo·u ˘s) adj. diligent, persevering,

suitable to what is being said or done. The chairman’s

unremitting; constant in application or attention. The

remarks referring to the founding fathers were apropos

nurses in the intensive care unit are known for providing

since it was the Fourth of July.

assiduous care to their patients.

arcane (ahr·'kayn) adj. mysterious, secret, beyond com-

assuage (a˘·'swayj) v. to make something less severe, to

prehension. A number of college students in the 1980s

soothe; to satisfy (as hunger or thirst). The small cups

became involved in the arcane game known as “Dun-

of water offered to the marathon runners helped to

geons and Dragons.”

assuage their thirst.

archaic (ahr·'kay·ik) adj. belonging to former or ancient

attenuate (a˘·'ten·yoo·ayt) v. 1. to make thin or slender

times; characteristic of the past. Samantha laughed at

2. to weaken, reduce in force, value, or degree. The

her grandfather’s archaic views of dating and

Russian army was able to attenuate the strength and

relationships.

number of the German forces by leading them inland

archetype ('ahr·ki·t¯p) n. an original model from which others are copied; original pattern or prototype. Elvis

during winter. audacious (aw·'day·shu ˘s) adj. fearlessly or recklessly

Presley served as the archetype for rock-and-roll per-

daring or bold; unrestrained by convention or propri-

formers in the 1950s.

ety. Detective Malloy’s methods were considered bold

ardor ('ahr·do ˘r) n. fiery intensity of feeling; passionate

and audacious by his superiors, and they often achieved

enthusiasm, zeal. The ardor Larry brought to the campaign made him a natural spokesperson.

results. august (aw·'ust) adj. majestic, venerable; inspiring

arduous ('ahr·joo·u ˘s) adj. 1. very difficult, laborious;

admiration or reverence. Jackie Kennedy’s august dig-

requiring great effort 2. difficult to traverse or sur-

nity in the days following her husband’s assassination

mount. Commander Shackleton’s arduous journey

set a tone for the rest of the nation as it mourned.

265

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

auspice ('aw·spis) n. 1. protection or support, patronage

harm 2. poison. The bane of the oak tree is the Asian

2. a forecast or omen. The children’s art museum was

beetle. beguile (bi·'¯l) v. to deceive or cheat through cunning; to

able to continue operating through the auspices of an anonymous wealthy benefactor.

distract the attention of, divert; to pass time in a

auspicious (aw·'spish·u ˘s) adj. favorable, showing signs

pleasant manner, to amuse or charm. Violet was able

that promise success; propitious. Valerie believed it an

to beguile the spy, causing him to miss his secret

auspicious beginning when it rained on the day that she

meeting. belie (bi·'l¯) v. 1. to give a false impression, misrepresent

opened her umbrella store. austere (aw·'steer) adj. 1. severe or stern in attitude or

2. to show to be false, to contradict. By wearing an

appearance 2. simple, unadorned, very plain. With its

expensive suit and watch, Alan hoped to belie his lack of

simple but functional furniture and its obvious lack of

success to everyone at the reunion. bellicose ('bel·˘·kohs) adj. belligerent, quarrelsome,

decorative elements, the interior of the Shaker meeting hall was considered austere by many people.

eager to make war. There was little hope for peace fol-

authoritarian (a˘·'thor·i·'tair·i·a˘n) adj. favoring com-

lowing the election of a candidate known for his belli-

plete, unquestioning obedience to authority as

cose nature. belligerent (bi·'lij·e ˘r·e ˘nt) adj. hostile and aggressive, show-

opposed to individual freedom. The military maintains an authoritarian environment for its officers and

ing an eagerness to fight. Ms. Rivera always kept an eye

enlisted soldiers alike.

on Daniel during recess, as his belligerent attitude often

avant-garde (a·vahnt·'ahrd) adj. using or favoring an

caused problems with other children.

ultramodern or experimental style; innovative, cutting-

bevy ('bev·ee) n. 1. a large group or assemblage 2. a flock

edge, especially in the arts or literature. Though it seems

of animals or birds. There was a lively bevy of eager

very conventional now, in the 1950s, Andy Warhol’s art

bingo fans waiting outside the bingo hall for the game to

was viewed as avant-garde.

begin.

aversion (a˘·'vur·zho ˘n) n. 1. a strong, intense dislike;

bilk (bilk) v. to deceive or defraud; to swindle, cheat, espe-

repugnance 2. the object of this feeling. Todd has an

cially to evade paying one’s debts. The stockbroker was

aversion to arugula and picks it out of his salads.

led away in handcuffs, accused of trying to bilk senior citizens out of their investment dollars. blasphemy ('blas·fe˘·mee) n. contemptuous or irreverent

B

acts, utterances, attitudes or writings against God or baleful ('bayl·fu ˘l) adj. harmful, menacing, destructive,

other things considered sacred; disrespect of some-

sinister. Whether it’s a man, woman, car, or animal,

thing sacrosanct. If you committed blasphemy during

you can be certain to find at least one baleful character

the Inquisition, the consequences were severe.

in a Stephen King horror novel.

blatant ('blay·tant) adj. completely obvious, not

banal (ba˘·'nal) adj. commonplace, trite; obvious and

attempting to conceal in any way. Samuel’s blatant dis-

uninteresting. Though Tom and Susan had hoped for

regard of the rules earned him a two-week suspension. blight (bl¯t) n. 1. a plant disease that causes the affected

an adventure, they found that driving cross-country on the interstate offered mostly banal sites, restaurants, and

parts to wilt and die 2. something that causes this

attractions.

condition, such as air pollution 3. something that

bane (bayn) n. 1. cause of trouble, misery, distress, or

impairs or destroys 4. an unsightly object or area.

266

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

They still do not know what caused the blight that

begin to sprout, grow new buds, blossom. The tulip

destroyed half of the trees in the orchard.

bulbs beneath the soil would burgeon in early spring

blithe (bl¯th) adj. light-hearted, casual, and carefree.

providing there was no late frost.

Rachel’s blithe attitude toward spending money left her

burnish ('bur·nish) v. to polish, rub to a shine. When

broke and in debt.

Kathryn began to burnish the old metal teapot, she real-

boisterous ('boi·ste˘·ru ˘s) adj. 1. loud, noisy, and lacking

ized that it was, in fact, solid silver.

restraint or discipline 2. stormy and rough. The boisterous crowd began throwing cups onto the field during

C

the football game. cabal (ka˘·'bal) n. 1. a scheme or conspiracy 2. a small

bolster ('bohl·ste˘r) v. 1. to support or prop up 2. to buoy or hearten. Coach Edmond’s speech bolstered the team’s

group joined in a secret plot. With Antonio as their

confidence.

leader, the members of the cabal readied themselves to

bombastic (bom·'bas·tik) adj. speaking pompously, with inflated self-importance. Ahmed was shocked that a

begin the uprising. cadge (kaj) v. to beg, to obtain by begging. Their dog Cleo

renowned and admired humanitarian could give such a

would cadge at my feet, hoping I would throw him some

bombastic keynote address.

table scraps. capricious (ka ˘·'prish·u ˘s) adj. impulsive, whimsical and

boor (boor) n. a crude, offensive, ill-mannered person. Seeing Chuck wipe his mouth with his sleeve, Maribel

unpredictable. Robin Williams, the comedian, demon-

realized she was attending her senior prom with a clas-

strates a most capricious nature even when he is not

sic boor.

performing.

bourgeois (boor·'zhwah) adj. typical of the middle class;

careen (ka˘·'reen) v. 1. to lurch from side to side while in

conforming to the standards and conventions of the

motion 2. to rush carelessly or headlong. Watching the

middle class. A house in the suburbs, two children, two

car in front of us careen down the road was very

cars, and three TVs are key indicators of a bourgeois

frightening.

lifestyle.

caste (kast) n. a distinct social class or system. While visit-

bravado (bra˘·'vah·doh) n. false courage, a show of pre-

ing India, Michael was fascinated to learn the particulars of each caste and the way they related to each other.

tended bravery. Kyle’s bravado often got him in trouble with other kids in the neighborhood.

castigate ('kas·t˘·ayt) v. to inflict a severe punishment on; to chastise severely. When she was caught stealing

broach (brohch) v. 1. to bring up, introduce, in order to begin a discussion of 2. to tap or pierce, as in to draw

for the second time, Maya knew her mother would casti-

off liquid. It was hard for Sarah to broach the subject of

gate her.

her mother’s weight gain.

catharsis (ka˘·'thahr·sis) n. the act of ridding or cleans-

˘s) adj. arrogant, conceited. The bumptious ('bump·shu

ing; relieving emotions via the experiences of others,

bumptious man couldn’t stop talking about himself or

especially through art. Survivors of war often experi-

looking in the mirror.

ence a catharsis when viewing Picasso’s painting Guer-

buoyant ('boi·a ˘nt) adj. 1. able to float 2. light-hearted,

nica, which depicts the bombing of a town during the

cheerful. In science class, the children tried to identify which objects on the table would be buoyant.

Spanish civil war. censure ('sen·shu ˘r) n. expression of strong criticism or

burgeon ('bur·jo ˘n) v. to begin to grow and flourish; to

disapproval; a rebuke or condemnation. After the sen-

267

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

consternation (kon·ste˘r·'nay·sho ˘n) n. a feeling of deep,

ator was found guilty of taking bribes, Congress unanimously agreed to censure him.

incapacitating horror or dismay. The look of conster-

chastise ('chas·t¯z) v. to punish severely, as with a beating; to

nation on the faces of the students taking the history

criticize harshly, rebuke. Charles knew that his wife would

exam alarmed the teacher, who thought he had pre-

chastise him after he inadvertently told the room full of

pared his students for the test. contentious (ko ˘n·'ten·shu ˘s) adj. 1. quarrelsome, com-

guests that she had just had a face lift. chauvinist ('shoh·v˘n·ist) n. a person who believes in

petitive, quick to fight 2. controversial, causing con-

the superiority of his or her own kind; an extreme

tention. With two contentious candidates on hand, it

nationalist. Though common in the early days of the

was sure to be a lively debate. conundrum (ko ˘·'nun·dru ˘m) n. a hard riddle, enigma; a

women’s movement, male chauvinists are pretty rare today.

puzzling question or problem. Alex’s logic professor

churlish ('chur·l˘sh) adj. ill-mannered, boorish, rude.

gave the class a conundrum to work on over the

Angelo’s churlish remarks made everyone at the table

weekend. ˘·'koh·pi·a) n. abundance; a horn of cornucopia (kor·nyu

uncomfortable and ill at ease. circumspect ('sur·ku ˘m·spekt) adj. cautious, wary,

plenty. The first graders made cornucopias for Thanks-

watchful. The captain was circumspect as she guided the

giving by placing papier-mache vegetables into a hol-

boat through the fog.

lowed-out horn. countenance ('kown·te˘·na˘ns) n. the appearance of a

coeval (koh·'ee·va˘l) adj. of the same time period, contemporary. The growth of personal computers and CD

person’s face, facial features and expression. As she

players were coeval during the late twentieth century.

walked down the aisle, Julia’s countenance was

cogent ('koh·je˘nt) adj. convincing, persuasive, com-

absolutely radiant.

pelling belief. Ella’s cogent arguments helped the debate

craven ('kray·ve˘n) adj. cowardly. “This craven act of violence will not go unpunished,” remarked the police chief.

team win the state championship.

credulous ('krej·u ˘·lu ˘s) adj. gullible, too willing to believe

collusion (ko ˘·'loo·zho ˘n) n. a secret agreement between two or more people for a deceitful or fraudulent pur-

things. All the tables, graphs, and charts made the com-

pose; conspiracy. The discovery of the e-mail proved

pany’s assets look too good to the credulous potential

that collusion existed between the C.E.O and C.F.O to

investors at the meeting.

defraud the shareholders. ˘m·'play·sa˘nt) adj. tending to comply, complaisant (ko

D

obliging, willing to do what pleases others. To preserve family peace and harmony, Lenny became very com-

daunt (dawnt) v. to intimidate, to make afraid or discour-

plaisant when his in-laws came to visit.

aged. Members of the opposing team were trying to

conciliatory (ko ˘n·'sil·ee·a ˘·tohr·ee) adj. making or willing

daunt the home team by yelling loudly and beating their

to make concessions to reconcile, soothe, or comfort;

chests. de facto (dee 'fak·toh) in reality or fact; actual. Though

mollifying, appeasing. Abraham Lincoln made conciliatory gestures toward the South at the end of the Civil War.

there was a ceremonial head of government, General

conclave ('kon·klav) n. a private or secret meeting. The double agent had a conclave with the spy she was sup-

Ashtononi was the de facto leader of the country. debacle (di·'bah·ke˘l) n. 1. a disaster or collapse; a total

posed to be observing.

defeat or failure 2. a sudden breaking up or breaking

268

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

loose; violent flood waters, often caused by the break-

derisive (di·'r¯·siv) adj. scornful, expressing ridicule;

ing up of ice in a river. The diplomatic talks became a

mocking, jeering. In order to promote productive dis-

debacle when the enemy state refused to negotiate.

cussion, derisive comments were forbidden in the

decimate ('des·˘·mayt) v. to destroy a large portion of.

classroom. derivative (di·'riv·a˘·tiv) adj. derived from another

Neglect and time would eventually decimate much of the housing in the inner cities.

source, unoriginal. The word “atomic” is a derivative of

decorum (di·'kohr·u ˘m) n. appropriateness of behavior,

the word “atom.”

propriety; decency in manners and conduct. When

desecrate ('des·e˘·krayt) v. to violate the sacredness of, to

questions concerning decorum arise, I always refer to

profane. Someone desecrated the local cemetery by

Emily Post.

spray-painting graffiti on tombstones. desultory (des·'u ˘l·tohr·ee) adj. aimless, haphazard;

deign (dayn) v. to condescend, to be kind or gracious enough to do something thought to be beneath one’s

moving from one subject to another without logical

dignity. Would you deign to spare a dime for a poor old

connection. The family became concerned listening to

beggar like me?

Steven’s desultory ramblings. ˘·mee) n. division into two usually dichotomy (d¯·'kot·o

delineate (di·'lin·ee·ayt) v. to draw or outline, sketch; to portray, depict, describe. The survey will clearly delin-

contradictory parts or kinds. When the teacher

eate where their property ends.

broached the subject of the election, there was a pre-

demagogue ('dem·a˘·aw) n. a leader who obtains power

dictable dichotomy among the students.

by appealing to people’s feelings and prejudices rather

diffident ('dif·i·de˘nt) adj. lacking self-confidence, shy

than by reasoning. Hilter was the most infamous dema-

and timid. Alan’s diffident nature is often misinter-

gogue of the twentieth century.

preted as arrogance. dilatory ('dil·a ˘·tohr·ee) adj. slow or late in doing some-

demur (di·'mur) v. to raise objections, hesitate. Polly hated to demur, but she didn’t think adding ten cloves of

thing; intended to delay, especially to gain time. Resent-

garlic to the recipe would taste good.

ful for having to work the holiday, Miguel’s dilatory approach to getting himself up and dressed was his own

demure (di·'myoor) adj. modest and shy, or pretending

small act of passive resistance.

to be so. When it was to her advantage, Sharon could be

disabuse (dis·a˘·'byooz) v. to undeceive, correct a false

very demure, but otherwise she was quite outgoing. denigrate ('den·i·rayt) v. to blacken the reputation of,

impression or erroneous belief. Natalie needed to disa-

disparage, defame. The movie script reportedly con-

buse Chin of his belief that she was in love with him.

tained scenes that would denigrate the queen, so those

disconcert (dis·ko ˘n·'surt) v. 1. to upset the composure of,

scenes were removed.

ruffle 2. to frustrate plans by throwing into disorder.

denouement (day·noo·'mahn) n. the resolution or clear-

The arrival of Miriam’s ex-husband and his new wife

ing up of the plot at the end of a narrative; the out-

managed to disconcert the typically unflappable Miriam.

come or solution of an often complex series of events.

disconsolate (dis·'kon·so ˘·lit) adj. 1. sad, dejected, disap-

The students sat at the edge of their seats as they listened

pointed 2. inconsolable, hopelessly unhappy. The dis-

to the denouement of the story.

consolate look on Peter’s face revealed that the letter

deprecate ('dep·re˘·kayt) v. to express disapproval of; to

contained bad news.

belittle, depreciate. Grandpa’s tendency to deprecate the

disenfranchise (dis·en·'fran·ch¯z) v. to deprive of the

children’s friends was a frequent source of family strife.

rights of citizenship, especially the right to vote. The

269

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

independent monitors were at polling locations to ensure

éclat (ay·'klah) n. conspicuous success; great acclaim or

neither party tried to disenfranchise incoming voters.

applause; brilliant performance or achievement. Even

disingenuous (dis·in·'jen·yoo·u ˘s) adj. 1. insincere, cal-

the ruinous deceit of the envious Salieri could not impede

culating; not straightforward or frank 2. falsely pre-

the dazzling éclat of the young and gifted Mozart. edifying ('ed·˘·f¯·in) adj. enlightening or uplifting with

tending to be unaware. Carl’s disingenuous comments were not taken seriously by anyone in the room.

the aim of improving intellectual or moral develop-

disparage (di·'spar·ij) v. to speak of in a slighting or

ment; instructing, improving. His edifying speech chal-

derogatory way, belittle. Comedians often disparage

lenged the community to devote more time to charitable

politicians as part of their comedic routines.

causes.

dissemble (di·'sem·be˘l) v. to disguise or conceal one’s

efficacious (ef·˘·'kay·shu ˘s) adj. acting effectively, pro-

true feelings or motives behind a false appearance.

ducing the desired effect or result. Margaret’s effica-

Tom needed to dissemble his desire for his boss’s job by

cious approach to her job in the collections department

acting supportive of her planned job change.

made her a favorite with the C.F.O. effrontery (i·'frun·te˘·ree) n. brazen boldness, impu-

dissuade (di·'swayd) v. to discourage from or persuade against a course of action. I tried to dissuade them

dence, insolence. The customs officials were infuriated

from painting their house purple, but they didn’t listen.

by the effrontery of the illegal alien who nonchalantly

dither ('dith·e˘r) v. 1. to hesitate, be indecisive and uncer-

carried drugs into the country in his shirt pocket. effusive (i·'fyoo·siv) adj. expressing emotions in an

tain 2. to shake or quiver. During a crisis, it is impor-

unrestrained or excessive way; profuse, overflowing,

tant to have a leader who will not dither. dogma ('daw·ma˘) n. a system of principles or beliefs, a

gushy. Anne’s unexpectedly effusive greeting made Tammy uncomfortable.

prescribed doctrine. Some find the dogma inherent in

egalitarian (i·al·i·'tair·ee·a˘n) adj. characterized by or

religion a comfort, whereas others find it too restrictive.

affirming the principle of equal political, social, civil,

dogmatic (daw·'ma·tik) adj. 1. asserting something in a positive, absolute, arrogant way 2. of or relating to

and economic rights for all persons. Hannah was

dogma. His dogmatic style of conversation was not very

moved by the candidate’s egalitarian speech. eke (eek) v. to get or supplement with great effort or strain;

popular with his young students. dross (draws) n. 1. waste product, sludge 2. something

to earn or accomplish laboriously. Working two jobs

worthless, commonplace, or trivial. Work crews immediately began the task of cleaning the dross at the aban-

enabled Quincy to eke out a living wage for his family. élan (ay·'lahn) n. 1. vivacity, enthusiasm, vigor 2. distinc-

doned plastics factory.

tive style or flair. The new designer’s élan and original-

dulcet ('dul·sit) adj. melodious, harmonious, sweet-

ity was sure to help him succeed in the highly

sounding. The chamber orchestra’s dulcet tunes were a perfect ending to a great evening.

competitive fashion industry. elite (i·'leet) n. 1. the best or most skilled members of a social group or class 2. a person or group regarded as

E

superior. Within the student orchestra, there existed a small group of musical elite who performed around the

ebullient (i·'bul·ye˘nt) adj. bubbling over with enthusiasm, exuberant. The ebullient children were waiting to

country. eloquent ('el·o ˘·kwe˘nt) adj. expressing strong emotions

stick their hands into the grab bag and pull out a toy.

or arguments in a powerful, fluent, and persuasive

270

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

ephemeral (i·'fem·e˘·ra˘l) adj. lasting only a very short

manner. Abraham Lincoln’s Gettysburg Address is considered one of the most eloquent speeches ever given by a

time, transitory. Numerous ephemeral ponds and pools

U.S. president.

can be found in the desert during the rainy season.

eminent ('em·˘·ne˘nt) adj. towering above or more promi-

epicurean (ep·i·'kyoor·ee·a˘n) n. a person devoted to

nent than others, lofty; standing above others in qual-

the pursuit of pleasure and luxury, especially the

ity, character, reputation, etc.; distinguished. The

enjoyment of good food and comfort. While on vaca-

chairperson proudly announced that the keynote speaker

tion at a posh resort hotel, Joan became a true

at the animal rights convention would be the eminent

epicurean. epitome (i·'pit·o ˘·mee) n. 1. something or someone that

primatologist Jane Goodall. empirical (em·'pir·i·kal) adj. based on observation or

embodies a particular quality or characteristic, a rep-

experience rather than theory. Frank’s empirical data

resentative example or a typical model 2. a brief sum-

suggested that mice would climb over the walls of the

mary or abstract. With his ten-gallon hat, western shirt,

maze to get to the cheese rather than navigate the maze

and rugged jeans, Alex was the epitome of the American

itself.

cowboy. equanimity (ee·kwa˘·'nim·i·tee) n. calmness of tempera-

enclave ('en·klayv) n. a distinct territory lying wholly within the boundaries of another, larger territory. The

ment, even-temperedness; patience and composure,

country of Lesotho is an enclave of South Africa.

especially under stressful circumstances. The hostage

endemic (en·'dem·ik) adj. 1. prevalent in or characteris-

negotiator’s equanimity during the standoff was

tic of a specific area or group of people 2. native to a

remarkable.

particular region. Kudzu, a hairy, purple-flowered vine

˘·kayt) v. to use unclear or ambiguequivocate (i·'kwiv·o

often thought to be endemic to the southeastern United

ous language in order to mislead or conceal the truth.

States, was actually imported from Japan.

Raj tried to equivocate when explaining why he came

enervate ('en·e˘r·vayt) v. to weaken, deprive of strength

home after his curfew. eradicate (i·'rad·˘·kayt) v. to root out and utterly

or vitality; to make feeble or impotent. Stephanie’s

destroy; to annihilate, exterminate. The exterminator

cutting remarks managed to enervate Hasaan. engender (en·'jen·de ˘r) v. to produce, give rise to, bring into

said he would eradicate the vermin from the house. erratic (i·'rat·ik) adj. 1. moving or behaving in an irregu-

existence. Professor Sorenson’s support worked to engen-

lar, uneven, or inconsistent manner 2. deviating from

der Samantha’s desire to pursue a Ph.D. enigma (e˘·'ni·ma˘) n. 1. something that is puzzling or

the normal or typical course of action, opinion, etc.

difficult to understand; a perplexing or inexplicable

During an earthquake, a seismograph’s needle moves in

thing that cannot be explained 2. a baffling problem

an erratic manner. erudite ('er·yu ˘·d¯t) adj. having or showing great learning;

or difficult riddle. How Winston came to be the president of this organization is a true enigma.

profoundly educated, scholarly. The scholarly work of

enormity (i·'nor·mi·tee) n. 1. excessive wickedness 2. a

nonfiction was obviously written by an erudite young

monstrous offense or evil act, atrocity. (Note: Enor-

author.

mity is often used to indicate something of great size

ethos ('ee·thos) n. the spirit, attitude, disposition or

(e.g., the enormity of the task), but this is considered

beliefs characteristic of a community, epoch, region,

an incorrect use of the word.) The enormity of the duo’s

etc. The ethos of their group included a commitment to

crimes will never be forgotten.

pacifism.

271

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

F

eulogy ('yoo·lo ˘·ee) n. a formal speech or piece of writing in praise of someone or something. Richard was asked to

facetious (fa˘·'see·shu ˘s) adj. humorous and witty, clev-

give a eulogy for his fallen comrade. euphoria (yoo·'fohr·ee·a˘) n. a feeling of well-being or

erly amusing; jocular, sportive. Ms. Weston’s facetious

high spirits. When falling in love, it is not uncommon

remarks always made people laugh. fatuous ('fach·oo·u ˘s) adj. complacently stupid; feeble-

to experience feelings of euphoria. evince (i·'vins) v. to show or demonstrate clearly; to make

minded and silly. Since Sam was such an intellectually

evident. The safety officer tried to evince the dangers of

accomplished student, Mr. Britt was surprised to dis-

driving under the influence by showing pictures of alco-

cover that Sam’s well-meaning but fatuous parents were

hol-related automobile accidents.

not at all like him.

exacerbate (i·'zas·e˘r·bayt) v. to make worse; to increase

feckless ('fek·lis) adj. 1. lacking purpose or vitality; fee-

the severity, violence, or bitterness of. You should have

ble, weak 2. incompetent and ineffective, careless.

known that splashing salt water on Dan’s wound would

Jake’s feckless performance led to his termination from

exacerbate his pain.

the team. fecund ('fek·u ˘nd) adj. fertile. The fecund soil in the valley

exculpate (eks·'kul·payt) v. to free from blame, to clear from a charge of guilt. When Anthony admitted to the

was able to sustain the growing community. feign (fayn) v. to pretend, to give the false appearance of.

crime, it served to exculpate Marcus. exigent ('ek·si·je˘nt) adj. 1. urgent, requiring immediate

Walter feigned illness to avoid attending the meeting. felicitous (fi·'lis·i·tu ˘s) adj. 1. apt, suitably expressed,

action or attention, critical 2. requiring much effort or precision, demanding. The late-night call on Paul’s

apropos 2. marked by good fortune. The felicitous

cell phone concerned matters of an exigent nature.

turn of events during her promotional tour propelled

exorbitant (i·'zor·bi·ta˘nt) adj. greatly exceeding the

Susan’s book to the bestseller list. fervent ('fur·e˘nt) adj. 1. having or showing great emotion;

bounds of what is normal or reasonable; inordinate and excessive. Three thousand dollars is an exorbitant

ardent, zealous 2. extremely hot, burning. Norman had

amount to pay for a scarf.

a fervent belief that aliens had already landed on earth.

expedient (ik·'spee·dee·e˘nt) adj. (1) appropriate for a

fervor ('fur·vo ˘r) n. zeal, ardor, intense emotion. The fer-

purpose, a suitable means to an end (2) serving to

vor of the fans in the stands helped propel the team to

promote one’s own interests rather than principle. A

victory. fetter ('fet·e˘r) v. 1. to shackle, put in chains 2. to impede

quick divorce was an expedient end to the couple’s twomonth marriage.

or restrict. The presence of two security guards fettered

expunge (ik·'spunj) v. to wipe or rub out, delete; to eliminate completely, annihilate. After finishing probation,

their plans to get backstage. flaccid ('fla-sid) adj. hanging loose or wrinkled; weak,

juveniles can petition the courts to expunge their crimi-

flabby, not firm. The skin of cadavers becomes flaccid in

nal records.

a matter of hours. flippant ('flip·a˘nt) adj. not showing proper seriousness;

extenuate (ik·'sten·yoo·ayt) v. to reduce the strength or lessen the seriousness of, to try to partially excuse.

disrespectful, saucy. Ursula’s flippant remarks in front

Fred claimed that extenuating circumstances forced him

of her fiancé’s parents were an embarrassment to us all.

to commit forgery.

florid ('flor·id) adj. 1. elaborate, ornate 2. (of complexion) ruddy, rosy. The florid architecture in Venice did

272

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

garrulous ('ar·u ˘·lu ˘s) adj. talkative. Andrew had the

not appeal to me; I prefer buildings without so much ornamentation.

unfortunate luck of being seated next to a garrulous

flout (flowt) v. to disobey openly and scornfully; to reject,

young woman for his 12-hour flight.

mock, go against (as in a tradition or convention). Flappers

genteel (jen·'teel) adj. elegantly polite, well-bred, refined.

in the early 20th century would flout convention by bobbing

The genteel host made sure that the entrées were cooked

their hair and wearing very short skirts.

to each guest’s specifications. gregarious (re˘·'air·ee·u ˘s) adj. 1. seeking and enjoying

forbearance (for·'bair·a˘ns) n. patience, willingness to wait, tolerance. Gustaf dreaded the security check in the

the company of others, sociable 2. tending to form a

airport, but he faced it with great forbearance because

group with others of the same kind. John was a gre-

he knew it was for his own safety.

garious fellow who always had fun at social events.

forestall (fohr·'stawl) v. to prevent by taking action first,

guffaw (u·'faw) n. a noisy, coarse burst of laughter.

preempt. The diplomat was able to forestall a conflict by

Michael let out quite a guffaw when Jamal told him the

holding secret meetings with both parties.

outlandish joke.

forswear (for·'swair) v. 1. to give up, renounce 2. to deny

guile (¯l) n. treacherous cunning; shrewd, crafty deceit.

under oath. Natasha had to forswear her allegiance to

The most infamous pirates displayed tremendous guile.

her homeland in order to become a citizen of the new country.

H

frugal ('froo·a˘l) adj. 1. careful and economical, sparing, thrifty 2. costing little. My grandparents survived the

hallow ('hal·oh) v. to make holy, consecrate. The religious

Great Depression by being very frugal.

leader proclaimed the new worship hall a hallowed space.

fulminate ('ful·m˘·nayt) v. 1. to issue a thunderous ver-

hapless ('hap·lis) adj. unlucky, unfortunate. The hapless

bal attack, berate 2. to explode or detonate. The sena-

circumstances of her journey resulted in lost luggage,

tor was prone to fulminating when other legislators

missed connections, and a very late arrival. harangue (ha˘·'ran) n. a long, often scolding or bombas-

questioned her ideology. fulsome ('ful·so ˘m) adj. offensive due to excessiveness,

tic speech; a tirade. Members of the audience began to get restless during the senator’s political harangue.

especially excess flattery or praise. Her new coworker’s

harbinger ('hahr·bin·je˘r) n. a person, thing, or event

fulsome attention bothered Kathryn.

that foreshadows or indicates what is to come; a forerunner or precursor. The arrival of the robins is a har-

G

binger of spring. harrowing ('har·oh·in) adj. distressing, creating great

gainsay ('ayn·say) v. to deny, contradict, or declare false; to oppose. Petra would gainsay all accusations

stress or torment. The turbulent flight proved to be a

made against her.

harrowing experience for Jane.

˘n) adj. gigantic, huge. It was a gargantuan (ahr·'an·choo·a

haughty ('haw·tee) adj. scornfully arrogant and conde-

gargantuan supermarket for such a small town.

scending; acting as though one is superior and others

garish ('air·ish) adj. excessively bright or overdecorated,

unworthy, disdainful. Stanley is so haughty that he has

gaudy; tastelessly showy. Though Susan thought Las Vegas was garish, Emily thought it was perfectly

very few friends. hegemony (hi·'jem·o ˘·nee) n. predominant influence or

beautiful.

leadership, especially of one government over others.

273

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

A military takeover in the impoverished country secured

impecunious (im·pe˘·'kyoo·nee·u ˘s) adj. having little or

the hegemony of the Centrist Party in its bid for power.

no money; poor, penniless. Many impecunious immi-

hermetic (hur·'met·ik) adj. having an airtight closure;

grants to the United States eventually were able to make

protected from outside influences. Astronauts go for

comfortable lives for themselves. imperialism (im·'peer·ee·a˘·liz·e˘m) n. the policy of

space walks only when wearing hermetic space suits.

extending the rule or authority of a nation or empire I

by acquiring other territories or dependencies. Great Britain embraced imperialism, acquiring so many terri-

iconoclast (¯·'kon·oh·klast) n. 1. a person who attacks

tories that the sun never set on the British Empire.

and seeks to overthrow traditional ideas, beliefs, or

imperious (im·'peer·ee·u ˘s) adj. overbearing, bossy,

institutions 2. someone who opposes and destroys

domineering. Stella was relieved with her new job

idols used in worship. Using words as weapons, the

transfer because she would no longer be under the con-

well-spoken iconoclast challenged religious hypocrisy

trol of such an imperious boss. impetuous (im·'pech·oo·u ˘s) adj. 1. characterized by sud-

and fanaticism wherever she found it. ignoble (i·'noh·be˘l) adj. 1. lacking nobility in character

den, forceful energy or emotion; impulsive, unduly

or purpose, dishonorable 2. not of the nobility, com-

hasty and without thought 2. marked by violent force.

mon. Mark was an ignoble successor to such a well-

It was an impetuous decision to run off to Las Vegas and

respected leader, and many members of the organization

get married after a one-week courtship. implacable (im·'plak·a˘·be˘l) adj. incapable of being pla-

resigned. ignominious (i·no ˘·'min·ee·u ˘s) adj. 1. marked by shame

cated or appeased; inexorable. Some of the people who

or disgrace 2. deserving disgrace or shame; despicable.

call the customer service desk for assistance are implaca-

The evidence of plagiarism brought an ignominious end

ble, but most are relatively easy to serve.

to what had been a notable career for the talented young

importune (im·por·'toon) v. 1. to ask incessantly, make incessant requests 2. to beg persistently and urgently.

author.

Children can’t help but importune during the holidays,

imbroglio (im·'brohl·yoh) n. a confused or difficult situation, usually involving disagreement. An imbroglio

constantly nagging for the irresistible toys they see

developed when the bus drivers went on strike, leaving

advertised on television.

thousands of commuters stranded at the bus station

imprecation (im·pre˘·'kay·sho ˘n) n. an invocation of evil, a curse. In the book I’m reading, the gypsy queen levies

with no way to get home. immolate ('im·o ˘·layt) v. 1. to kill, as a sacrifice 2. to kill or destroy by fire. After the relationship ended, she chose to

an imprecation on the lead character. impudent ('im·pyu ˘·de˘nt) adj. 1. boldly showing a lack of respect, insolent 2. shamelessly forward, immod-

immolate the letters they had exchanged. impasse ('im·pas) n. a deadlock, stalemate; a difficulty

est. Thumbing his nose at the principal was an impu-

without a solution. The labor negotiations with management reached an impasse, and a strike seemed

dent act. impute (im·'pyoot) v. to attribute to a cause or source,

imminent.

ascribe, credit. Doctors impute the reduction in cancer

impassive (im·'pas·iv) adj. not showing or feeling emo-

deaths to the nationwide decrease in cigarette smoking.

tion or pain. It was hard to know what she was feeling

incendiary (in·'sen·dee·er·ee) adj. 1. causing or capable

by looking at the impassive expression on her face.

of causing fire; burning readily 2. of or involving

274

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

arson 3. tending to incite or inflame, inflammatory.

no surprise that he was viewed as a heathen and an

Fire marshals checked for incendiary devices in the the-

infidel by his family when he refused to be married in

ater after they received an anonymous warning.

the church. ingenuous (in·'jen·yoo·u ˘s) adj. 1. not cunning or deceit-

inchoate (in·'koh·it) adj. 1. just begun; in an initial or early stage of development, incipient 2. not yet fully

ful, unable to mask feelings; artless, frank, sincere 2.

formed, undeveloped, incomplete. During the

lacking sophistication or worldliness. (Note: Do not

inchoate stage of fetal growth, it is difficult to distin-

confuse with ingenious, meaning “remarkably clever.”)

guish between a cow, a frog, or a human; as they

Don’s expression of regret was ingenuous, for even

mature, the developing embryos take on the characteris-

though he didn’t know her well, he felt a deep sadness

tics of their own particular species.

when Mary died.

incredulous (in·'krej·u ˘·lu ˘s) adj. skeptical, unwilling to

inimitable (i·'nim·i·ta˘·be˘l) adj. defying imitation,

believe. (Note: Do not confuse with incredible, mean-

unmatchable. His performance on the tennis court was

ing “implausible or beyond belief.”) The members of

inimitable, and he won three championships. inscrutable (in·'scroo·ta ˘·be˘l) adj. baffling, unfathomable,

the jury were incredulous when they heard the defendant’s far-fetched explanation of the crime.

incapable of being understood. It was completely

incursion (in·'kur·zho ˘n) n. a raid or temporary invasion

inscrutable how the escape artist got out of the trunk.

of someone else’s territory; the act of entering or run-

insolent ('in·so ˘·le˘nt) adj. haughty and contemptuous;

ning into a territory or domain. There was an incur-

brazen, disrespectful, impertinent. Parents of teenagers

sion on the western border of their country.

often observe the insolent behavior that typically accom-

indefatigable (in·di·'fat·˘·a˘·be˘l) adj. not easily

panies adolescence. insouciant (in·'soo·see·a ˘nt) adj. unconcerned, carefree,

exhausted or fatigued; tireless. The indefatigability of the suffragette movement led to the passage of the 19th

indifferent. Wendy’s insouciant attitude toward her future

Amendment, guaranteeing women the right to vote.

concerned her father, who expected her to go to college.

indolent ('in·do ˘·le˘nt) adj. 1. lazy, lethargic, inclined to

interdict (in·te˘r·'dikt) v. to prohibit, forbid. Carlos

avoid labor 2. causing little or no pain; slow to grow

argued that the agriculture department should interdict

or heal. Iris’s indolent attitude did not bode well for her

plans to produce genetically modified foods. intractable (in·'trak·ta˘·be˘l) adj. unmanageable, unruly,

professional future. indomitable (in·'dom·i·ta˘·be˘l) adj. not able to be van-

stubborn. The young colt was intractable, and training

quished or overcome, unconquerable; not easily dis-

had to be cancelled temporarily. intransigent (in·'tran·si·je˘nt) adj. unwilling to compro-

couraged or subdued. The indomitable spirit of the Olympic athletes was inspirational.

mise, stubborn. Young children can be intransigent

ineluctable (in·i·'luk·ta˘·be˘l) adj. certain, inevitable; not

when it comes to what foods they will eat, insisting on

to be avoided or overcome. The ineluctable outcome of

familiar favorites and rejecting anything new.

the two-person race was that there would be one winner

intrepid (in·'trep·id) adj. fearless, brave, undaunted. The

and one loser.

intrepid nature and fortitude of the U.S. Marines is

infidel ('in·fi·de˘l) n. 1. a person with no religious beliefs 2. a non-believer, one who does not accept a particu-

legendary. inured (in·'yoord) adj. accustomed to, adapted. Trisha

lar religion, doctrine, or system of beliefs. Because

had become inured to her boss’s criticism, and it no

Tom had been raised with strict religious beliefs, it was

longer bothered her.

275

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

inveigle (in·'vay·e˘l) v. 1. to influence or persuade

affairs. I believe a more laissez-faire approach by man-

through gentle coaxing or flattery; to entice. Vanessa

agement would make everyone more cooperative and

inveigled her way into a promotion that should have

productive. libertine ('lib·e˘r·teen) n. one who lives or acts in an

gone to Marie. inveterate (in·'vet·e˘·rit) adj. habitual; deep rooted,

immoral or irresponsible way; one who acts according

firmly established. I am an inveterate pacifist and am

to his or her own impulses and desires and is unre-

unlikely to change my mind.

strained by conventions or morals. They claim to be

involute ('in·vo ˘·loot) adj. intricate, complex. The tax

avant-garde, but in my opinion, they’re just a bunch of

reform committee faces an extremely involute problem if

libertines. lilliputian (lil·i·'pyoo·sha˘n) adj. 1. very small, tiny 2.

it wants to distribute the tax burden equally. iota (¯·'oh·ta˘) n. a very small amount; the smallest possi-

trivial or petty. My troubles are lilliputian compared to

ble quantity. Professor Carlton is so unpopular because

hers, and I am thankful that I do not have such major

he doesn’t have one iota of respect for his students.

issues in my life.

irascible (i·'ras·˘·be˘l) adj. irritable, easily aroused to

loquacious (loh·'kway·shu ˘s) adj. talkative, garrulous.

anger, hot tempered. Her irascible temperament caused

The loquacious woman sitting next to me on the six-

many problems with the staff at the office.

hour bus ride talked the entire time.

ire (¯r) n. anger, wrath. I was filled with ire when Vladimir

lucid ('loo·sid) adj. 1. very clear, easy to understand, intelligible 2. sane or rational. Andrea presented a very

tried to take credit for my work.

lucid argument that proved her point beyond a shadow

irk (urk) v. to annoy, irritate, vex. Being a teenager means

of a doubt.

being continually irked by your parents—and vice

lucrative ('loo·kra˘·tiv) adj. profitable, producing much

versa. ˘·loot) adj. feeling or showing uncerirresolute (i·'rez·o

money. Teaching is a very rewarding career, but unfor-

tainty; hesitant, indecisive. Sandra is still irresolute, so

tunately it is not very lucrative.

if you talk to her, you might help her make up her mind.

lugubrious (luu·'oo·bree·u ˘s) adj. excessively dismal or mournful, often exaggeratedly or ridiculously so. Billy

J

looks like a fool, acting so lugubrious over losing a silly bet.

jocund ('jok·u ˘nd) adj. merry, cheerful; sprightly and

M

lighthearted. Alexi’s jocund nature makes it a pleasure maladroit (mal·a˘·'droit) adj. clumsy, bungling, inept.

to be near her.

The maladroit waiter broke a dozen plates and spilled L

coffee on two customers. malaise (ma˘·'layz) n.a feeling of illness or unease. After

laconic (la˘·'kon·ik) adj. brief, to the point, terse. Morri-

his malaise persisted for more than a week, Nicholas

son’s ten-minute commencement address was every-

went to see a doctor. malapropism ('mal·a˘·prop·iz·e˘m) n. comical misuse of

thing you could have asked for: laconic, powerful, and inspirational.

words, especially those that are similar in sound. His

laissez-faire (les·ay 'fair) adj. hands-off policy; noninterference by the government in business and economic

malapropisms may make us laugh, but they won’t win our vote.

276

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

malfeasance (ma˘l·'fee·za˘ns) n. misconduct or wrongdo-

mince (mins) v. 1. to cut into very small pieces 2. to walk

ing, especially by a public official; improper profes-

or speak affectedly, as with studied refinement 3. to

sional conduct. The city comptroller was found guilty of

say something more delicately or indirectly for the

malfeasance and removed from office.

sake of politeness or decorum. Please don’t mince your

malinger (ma˘·'lin·e˘r) v. to pretend to be injured or ill

words—just tell me what you want to say.

in order to avoid work. Stop malingering and give me a

minutiae (m˘·no¯o¯'she¯·a) n., pl. very small details; trivial

hand with this job.

or trifling matters. His attention to the minutiae of the

malleable ('mal·ee·a˘·be˘l) adj. 1. easily molded or pressed into shape 2. easily controlled or influenced 3. easily

process enabled him to make his great discovery. mirth (murth) n. great merriment, joyous laughter. The

adapting to changing circumstances. You should be

joyous wedding celebration filled the reception hall with

able to convince Xiu quickly; she’s quite a malleable

mirth throughout the evening.

person.

misanthrope ('mis·an·throhp) n. one who hates or dis-

maverick ('mav·e˘r·ik) n. rebel, nonconformist, one who

trusts humankind. Pay no mind to his criticism; he’s a

acts independently. Madonna has always been a mav-

real misanthrope, and no one can do anything right in

erick in the music industry.

his eyes. miscreant ('mis·kree·a˘nt) n. a villain, criminal; evil per-

mélange (may·'lahnzh) n. a mixture or assortment. There was a very interesting mélange of people at the

son. The miscreant had eluded the police for months,

party.

but today he was finally captured. mitigate ('mit·˘·ayt) v. 1. to make less intense or severe

mellifluous (me·'lif·loo·u ˘s) adj. sounding sweet and flowing; honeyed. Her mellifluous voice floated in

2. to moderate the force or intensity of, soften, dimin-

through the windows and made everyone smile.

ish, alleviate. The unusual extenuating circumstances

mendacity (men·'das·i·tee) n. 1. the tendency to be dis-

mitigated her punishment. mollify ('mol·˘·f¯) v. 1. to soothe the anger of, calm 2. to

honest or untruthful 2. a falsehood or lie. Carlos’s mendacity has made him very unpopular with his class-

lessen in intensity 3. to soften, make less rigid. The

mates, who don’t feel they can trust him.

crying child was quickly mollified by her mother.

mercurial (me˘r·'kyoor·ee·a˘l) adj. 1. liable to change

moot (moot) adj. debatable, undecided. Although this is a

moods suddenly 2. lively, changeable, volatile. Fiona is

moot issue, it is one that is often debated among certain

so mercurial that you never know what kind of reaction

circles. morose (mo ˘·'rohs) adj. gloomy, sullen, melancholy. My

to expect. meretricious (mer·e˘·'trish·u ˘s) adj. gaudy, tawdry; showily attractive but false or insincere. With its casinos and

daughter has been morose ever since our dog ran away. ˘s) adj. very varied, greatly multifarious (mul·ti·'fair·ee·u

attractions, some people consider Las Vegas the most

diversified; having many aspects. The job requires the

meretricious city in the country.

ability to handle multifarious tasks.

mete (meet) v. to distribute, allot, apportion. The punish-

mundane (mun·'dayn) adj. 1. dull, routine; common-

ments were meted out fairly to everyone involved in the plot. mettlesome ('met·e˘l·so ˘m) adj. courageous, high-spir-

place, ordinary 2. worldly as opposed to spiritual. My job may be mundane, but it is secure and it pays well.

ited. (Note: Do not confuse with meddlesome, meaning inclined to interfere.) Alice’s mettlesome attitude was infectious and inspired us all to press on.

277

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

N

O obdurate ('ob·du ˘·rit) adj. stubborn and inflexible; hard-

nadir ('nay·d˘r) n. the very bottom, the lowest point. When he felt he was at the nadir of his life, Robert

hearted, not easily moved to pity. I doubt he’ll change

began to practice mediation to elevate his spirits.

his mind; he’s the most obdurate person I know.

narcissism ('narh·si·siz·e˘m) n. admiration or worship of

obfuscate ('ob·fus·kayt) v. 1. to make obscure or

oneself; excessive interest in one’s own personal fea-

unclear, to muddle or make difficult to understand 2.

tures. Some critics say that movie stars are guilty of

to dim or darken. Instead of clarifying the matter, Wal-

narcissism.

ter only obfuscated it further. obstreperous (ob·'strep·e˘·ru ˘s) adj. noisily and stub-

nascent ('nas·e˘nt) adj. coming into existence, emerging. The nascent movement gathered strength quickly and

bornly defiant; aggressively boisterous, unruly. The

soon became a nationwide call to action.

obstreperous child refused to go to bed.

nemesis ('nem·e˘·sis) n. 1. source of harm or ruin, the

obtrusive (o ˘b·'troo·siv) adj. 1. prominent, undesirably

cause of one’s misery or downfall; bane 2. agent of ret-

noticeable 2. projecting, thrusting out 3. tending to

ribution or vengeance. In Frankenstein, the monster

push one’s self or one’s ideas upon others, forward,

Victor creates becomes his nemesis.

intrusive. Thankfully, Minsun survived the accident,

nexus ('nek·su ˘s) n. 1. a means of connection, a link or tie

but she was left with several obtrusive scars. obtuse (o ˘b·'toos) adj. 1. stupid and slow to understand 2.

between a series of things 2. a connected series or group 3. the core or center. The nexus between the lob-

blunt, not sharp or pointed. Please don’t be so obtuse;

byists and the recent policy changes is clear.

you know what I mean.

noisome ('noi·so ˘m) adj. 1. offensive, foul, especially in

obviate ('ob·vee·ayt) v. to make unnecessary, get rid of.

odor; putrid 2. harmful, noxious. What a noisome

Hiring Magdalena would obviate the need to hire a

odor is coming from that garbage can!

music tutor, for she is also a classical pianist.

non sequitur (non 'sek·wi·tu ˘r) n. a conclusion that does

occult (o ˘·'kult) adj. 1. secret, hidden, concealed 2. involv-

not logically follow from the evidence. Marcus’s argu-

ing the realm of the supernatural 3. beyond ordinary

ment started off strong, but it degenerated into a series

understanding, incomprehensible. The rites and beliefs

of non sequiturs.

of the occult organization were finally made a matter of

nonchalant (non·sha˘·'lahnt) adj. indifferent or cool, not showing anxiety or excitement. Victoria tried to be

public record after a long investigation. odious ('oh·di·u ˘s) adj. contemptible, hateful, detestable.

nonchalant, but I could tell she was nervous.

This is an odious policy that will only damage the envi-

noxious ('nok·shu ˘s) adj. unpleasant and harmful, unwholesome. The noxious smell drove everyone from

ronment more. officious (o ˘·'fish·u ˘s) adj. meddlesome, bossy; eagerly

the room.

offering unnecessary or unwanted advice. My officious

nullify ('nul·˘·f¯) v. 1. to make null (without legal force),

Aunt Midge is coming to the party, so be prepared for

invalidate 2. to counteract or neutralize the effect of. The opponents wanted to nullify the bill before it

lots of questions and advice. oligarchy ('ol·˘·ahr·kee) n. form of government in

became a law.

which the power is in the hands of a select few. The small governing body calls itself a democracy, but it is clearly an oligarchy.

278

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

omnipotent (om·'nip·o ˘·te˘nt) adj. having unlimited or

spin on 2. to provide relief from pain, relieve the

universal power or force. In Greek mythology, Zeus was

symptoms of a disease or disorder. The governor tried

the most powerful god, but he was not omnipotent, since

to palliate his malfeasance, but it soon became clear that

even his rule was often held in check by the unchange-

he would not be able to prevent a scandal. pallor ('pal·o ˘r) n. paleness, lack of color. The fever sub-

able laws of the Three Fates. omniscient (om·'nish·e ˘nt) adj. having infinite knowledge;

sided, but her pallor remained for several weeks. paradigm ('par·a˘·d¯m) n. 1. something that serves as a

knowing all things.In a story with an omniscient narrator, you can hear the thoughts and feelings of all of the characters.

model or example 2. set of assumptions, beliefs, val-

onus ('oh·nu ˘s) n. duty or responsibility of doing some-

ues or practices that constitutes a way of understand-

thing; task, burden. It was Clark’s idea, so the onus is

ing or doing things. Elected “Employee of the Month,”

on him to show us that it will work.

Winona is a paradigm of efficiency.

opprobrious (o ˘·'proh·bree·u ˘s) adj. 1. expressing con-

pariah (pa˘·'r¯·a˘) n. an outcast, a rejected and despised

tempt or reproach; scornful, abusive 2. bringing

person. After he told a sexist joke, Jason was treated like

shame or disgrace. It was inappropriate to make such

a pariah by all of the women in the office. partisan ('pahr·ti·za˘n) n. 1. a person fervently and often

opprobrious remarks in front of everybody. opulent ('op·yu ˘·le˘nt) adj. 1. possessing great wealth,

uncritically supporting a group or cause 2. a guerilla,

affluent 2. abundant, luxurious. Lee is very wealthy,

a member of an organized body of fighters who attack

but he does not live an opulent lifestyle.

or harass an enemy. The partisan lobby could not see

ostensible (o·'sten·s˘·be˘l) adj. seeming, appearing as

the logic of the opposing senator’s argument and did not

such, put forward (as of a reason) but not necessarily

understand how the proposed legislation would infringe

so; pretended. The ostensible reason for the meeting is

upon basic constitutional rights.

to discuss the candidates, but I believe they have already

paucity ('paw·si·tee) n. scarcity, smallness of supply or quantity. The paucity of food in the area drove the herd

made their decision. ostracize ('os·tra˘·s¯z) v. to reject, cast out from a group

farther and farther to the south. peccadillo (pek·a˘·'dil·oh) n. a trivial offense, a small sin

or from society. Kendall was ostracized after he repeatedly stole from his friends.

or fault. Don’t make such a big deal out of a little

overweening (oh·ve˘r·'wee·nin) adj. 1. presumptuously

peccadillo. pedantic (pi·'da˘n·tik) adj. marked by a narrow, tiresome

arrogant, overbearing 2. excessive, immoderate. I quit because I couldn’t stand to work for such an overween-

focus on or display of learning, especially of rules or

ing boss.

trivial matters. Her lessons were so pedantic that I

oxymoron (oks·ee·'moh·ro ˘n) n. a figure of speech con-

found I was easily bored. pedestrian (pe˘·'des·tri· a˘n) adj. commonplace, trite;

taining a seemingly contradictory combination of expressions. The term “non-working mother” is a con-

unremarkable, unimaginative, dull. Although the film

temptible oxymoron.

received critical acclaim, its pedestrian plot has been overused by screenwriters for decades. pellucid (pe˘·'loo·sid) adj. 1. translucent, able to be seen

P

through with clarity 2. (e.g., of writing) very clear, palliate ('pal·ee·ayt) v. 1. to make something less intense

easy to understand. Senator Waterson’s pellucid argu-

or severe, mitigate, alleviate; to gloss over, put a positive

279

ment made me change my vote.

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

petulant ('pech·u ˘·la˘nt) adj. peevish; unreasonably or

penchant ('pen·cha ˘nt) n. a strong inclination or liking. I have a real penchant for science fiction and spend hours

easily irritated or annoyed. The pouting and sulking

reading my favorite authors every night.

child could only be described as petulant!

penultimate (pi·'nul·t˘·mit) adj. next to last. There’s a

philistine ('fil·i·steen) n. a smug, ignorant person; some-

real surprise for the audience in the penultimate scene.

one who is uncultured and commonplace. Richards

penury ('pen·yu ˘·ree) n. extreme poverty, destitution.

thinks he is cosmopolitan, but he’s really just a

After ten years of penury, it’s good to be financially

philistine.

secure again.

phoenix ('fee·niks) n. 1. a person or thing of

peremptory (pe˘·'remp·to ˘·ree) adj. 1. offensively self-

unmatched beauty or excellence 2. a person or thing

assured, dictatorial 2. commanding, imperative, not

that has become renewed or restored after suffering

allowing contradiction or refusal 3. putting an end to

calamity or apparent annihilation (after the mytho-

debate or action. The father’s peremptory tone ended

logical bird that periodically immolated itself and

the children’s bickering.

rose from the ashes as a new phoenix). The phoenix

perfidious (pe˘r·'fid·ee·u ˘s) adj. treacherous, dishonest;

is often used to symbolize something that is

violating good faith, disloyal. The perfidious knight

indomitable or immortal.

betrayed his king.

pillage ('pil·ij) v. to forcibly rob of goods, especially in

perfunctory (pe˘r·'funk·to ˘·ree) adj. done out of a sense

time of war; to plunder. The barbarians pillaged the village before destroying it with fire.

of duty or routine but without much care or interest;

piquant ('pee·ka˘nt) adj. 1. agreeably pungent, sharp or

superficial, not thorough. We were not satisfied with his perfunctory work; we felt a more thorough job could

tart in taste 2. pleasantly stimulating or provocative.

have been done.

The spicy shrimp salad is wonderfully piquant.

˘·ree) n. the deliberate willful giving of perjury ('pur·ju

pique (peek) v. to wound (someone’s) pride, to offend; to

false, misleading, or incomplete testimony while

arouse or provoke. The article really piqued my interest

under oath. William was convicted of perjury for lying

in wildlife preservation.

about his whereabouts on the night of the crime.

pith (pith) n. 1. the essential or central part; the heart or

pernicious (pe˘r·'nish·u ˘s) adj. deadly, harmful, very

essence (of the matter, idea, experience, etc.) 2. (in

destructive. Nancy’s opponent started a pernicious

biology) the soft, sponge-like central cylinder of the

rumor that destroyed her chances of winning.

stems of most flowering plants. Her brief, but concise,

personable ('pur·so ˘·na˘·be˘l) adj. pleasing in appearance

statement went right to the pith of the argument and

or manner, attractive. Sandra is personable and well-

covered the most important issues.

liked by her peers.

placid ('plas·id) adj. calm and peaceful; free from distur-

pertinacious (pur·t˘·'nay·shu ˘s) adj. extremely stubborn or

bance or tumult. Lake Placid is as calm and peaceful as

persistent; holding firmly to a belief, purpose, or course

its name suggests.

of action. The pertinacious journalist finally uncovered

plaintive ('playn·tiv) adj. expressing sorrow; mournful,

the truth about the factory’s illegal disposal of toxins.

melancholy. Janice’s plaintive voice made me decide to

petrify ('pet·r˘·f¯) v. 1. to make hard or stiff like a stone

stay and comfort her longer.

2. to stun or paralyze with fear, astonishment, or

platitude ('plat·i·tood) n. a trite or banal statement,

dread. I was petrified when I heard the door open in the

especially one uttered as if it were new. Matthew

middle of the night.

offered me several platitudes but no real advice.

280

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

plethora ('pleth·o ˘·ra) n. an overabundance, extreme

prodigal ('prod·˘·a˘l) adj. 1. recklessly wasteful or

excess. There was a plethora of food at the reception.

extravagant, especially with money 2. given in great

poignant ('poin·ya ˘nt) adj. 1. arousing emotion, deeply

abundance, lavish or profuse. The parable of the prodi-

moving, touching 2. keenly distressing; piercing or

gal son shows what can happen when money is wasted. profligate ('prof·l˘·it) adj. 1. recklessly wasteful or

incisive. They captured the poignant reunion on film. polemical (po ˘·'lem·ik·a˘l) adj. controversial, argumenta-

extravagant, prodigal 2. lacking moral restraint, dis-

tive. The analyst presented a highly polemical view of

solute. The profligate man quickly depleted his

the economic situation.

fortune. proletariat (proh·le ˘·'tair·ee·a ˘t) n. the working class, those

poseur (poh·'zur) n. someone who takes on airs to impress others; a phony. My first impression of the arrogant new-

who do manual labor to earn a living. The proletariats

comer told me that he was a poseur; I just had a hunch that

demanded fewer hours and better wages.

he wasn’t what he seemed to be.

propinquity (proh·'pin·kwi·tee) n. 1. proximity, near-

pragmatic (pra·'mat·ik) adj. practical, matter-of-fact; favor-

ness 2. affinity, similarity in nature. The two scientific

ing utility. Since you don’t have money or time to waste, I

elements demonstrate a remarkable propinquity. propitious (proh·'pish·u ˘s) adj. auspicious, presenting

think you should take the most pragmatic approach. precarious (pri·'kair·ee·u ˘s) adj. 1. fraught with danger 2.

favorable circumstances. These are propitious omens

dangerously unsteady or insecure. Between hang-glid-

indeed and foretell a good journey.

ing and rock-climbing, Abram is constantly placing

prosaic (proh·'zay·ik) adj. unimaginative, ordinary, dull.

himself in very precarious positions.

The prosaic novel was rejected by the publisher. proscribe (proh·'skr¯b) v. 1. to prohibit, forbid; to ban-

precept ('pree·sept) n. a rule establishing standards of conduct. The headmaster reviewed the precepts of the

ish or outlaw 2. to denounce or condemn. The king

school with the students.

proscribed the worship of idols in his kingdom.

precipitous (pri·'sip·i·tu ˘s) adj. 1. extremely steep, drop-

protean ('proh·tee·a˘n) adj. taking many forms, change-

ping sharply 2. hasty, rash, foolhardy. Driving through

able; variable, versatile. In Native American mythology,

the state park, you spotted a grizzly bear on a precipi-

the coyote is often called the “shape shifter” because he is

tous cliff and wondered if he would fall.

such a protean character.

pretentious (pri·'ten·shu ˘s) adj. showy, pompous, putting

protocol ('proh·to ˘·kawl) n. 1. etiquette, ceremony, or

on airs. Hannah thinks that being pretentious will make

procedure with regard to people’s rank or status 2. a

people like her, but she is sorely mistaken.

first copy of a treaty or document. Jackson was fired for

prevaricate (pri·'var·˘·kayt) v. to tell lies, to stray from

repeatedly refusing to follow protocol.

or evade the truth. Quit prevaricating and tell me what

provident ('prov·i·de˘nt) adj. wisely providing for future

really happened.

needs; frugal, economical. Because my parents were so

primeval (pr¯·'mee·va˘l) adj. ancient, original, belonging

provident, I didn’t have to struggle to pay for college.

to the earliest ages. The primeval art found in the caves

proxy ('prok·see) n. 1. a person or agent authorized to represent or act for another 2. a document authoriz-

was discovered by accident. pristine (pris·'teen) adj. 1. in its original and unspoiled

ing this substitution. The president appointed a proxy

condition, unadulterated 2. clean, pure, free from contamination. We were awed by the beauty of the pristine

to handle business matters during his absence. puerile ('pyoo ˘·r˘l) adj. 1. childish, immature 2. suitable

forest in northern Canada.

only for children, belonging to or of childhood.

281

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

quiescent (kwi·'es·e˘nt) adj. inactive, quiet, at rest; dor-

Andrew is a remarkably successful businessman for someone so puerile.

mant, latent. The volcano is quiescent at the moment,

pugnacious (pu·'nay·shu ˘s) adj. contentious, quarrel-

but who knows when it will erupt again. quintessence (kwin·'tes·e˘ns) n. 1. the essence of a sub-

some, eager to fight, belligerent. Don’t be so pugnacious—I don’t want to fight.

stance 2. the perfect example or embodiment of

punctilious (punk·'til·i·u ˘s) adj. very conscientious and

something. Maura is the quintessence of kindness.

precise, paying great attention to details or trivialities,

quixotic (kwik·'sot·ik) adj. extravagantly chivalrous and

especially in regard to etiquette. Kira is as punctilious

unselfish; romantically idealistic, impractical. His

in her personal affairs as she is in the workplace.

quixotic ways charmed all the women at the dance. quotidian (kwoh·'tid·ee·a˘n) adj. 1. daily 2. common-

pundit ('pun·dit) n. a learned person or scholar; one who is an authority on a subject. The journalist consulted several

place, pedestrian. Prudence took her quotidian dose of

legal pundits before drafting the article.

medicine.

pungent ('pun·je˘nt) adj. 1. having a strong, sharp taste or smell 2. penetrating, caustic, stinging. I love the pun-

R

gent taste of a good, strong curry. purloin (pu ˘r·'loin) v. to steal. The thief purloined a sculp-

rakish ('ray·kish) adj. 1. debonair, smartly dressed or mannered, jaunty in appearance or manner 2. uncon-

ture worth thousands of dollars.

ventional and disreputable; dissolute or debauched.

purport (pur·'pohrt) v. 1. to be intended to seem, to have the appearance of being 2. propose or intend.

The rakish young woman charmed everyone at the

The letter purports to express your opinion on

table. rancor ('ran·ko ˘r) n. a bitter feeling of ill will, long-lasting

the matter.

resentment. Greg is full of rancor toward his brother, and this causes tension at family gatherings.

Q

rapacious (ra˘·'pay·shu ˘s) adj. excessively greedy and quaff (kwahf) v. to drink hurriedly or heartily; to swallow

grasping (especially for money); voracious, plunder-

in large draughts. He quickly quaffed three glasses of

ing. The rapacious general ordered his soldiers to pillage

water.

the town. raucous (raw-ku ˘s) adj. 1. unpleasantly loud and harsh 2.

quail (kwayl) v. to draw back in fear, flinch, cower. Mona

boisterous, disorderly, disturbing the peace. The rau-

quailed as soon as Otto entered the room. ˘·lu ˘s) adj. complaining, peevish, disquerulous ('kwer·u

cous music kept us awake all night.

contented. He’s a cantankerous and querulous old man,

reactionary (ree·'ak·sho ˘·ner·ee) n. a person who favors

but I love him.

political conservativism; one who is opposed to

queue (kyoo) n. 1. a line of people or vehicles waiting

progress or liberalism. It should be an interesting mar-

their turn 2. a pigtail. Look how long the queue is! We’ll

riage: he’s a reactionary and she’s as liberal as they

be waiting for hours.

come.

quid pro quo (kwid proh 'kwoh) n. a thing given in

recalcitrant (ri·'kal·si·tra˘nt) adj. disobedient, unruly,

return for something; an equal exchange or substitu-

refusing to obey authority. The recalcitrant child

tion. Let’s come up with a quid pro quo arrangement

was sent to the principal’s office for the third time

that will create a win-win situation for both sides.

in a week.

282

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

recidivism (ri·'sid·˘·vizm) n. a relapse or backslide, espe-

reprieve (ri·'preev) n. 1. postponement or cancellation of

cially into antisocial or criminal behavior after con-

punishment, especially of the death sentence 2. tem-

viction and punishment. Allowing prisoners to earn

porary relief from danger or discomfort. The court

their GED or a college degree has been shown to greatly

granted him a reprieve at the last moment because of

reduce recidivism.

DNA evidence that absolved him. reprisal (ri·'pr¯·za˘l) n. 1. an act of retaliation for an

recondite ('rek·o ˘n·d¯t) adj. 1. not easily understood, obscure, and abstruse 2. dealing with abstruse or pro-

injury with the intent of inflicting at least as much

found matters. He loves the challenge of grasping a rec-

harm in return 2. the practice of using political or

ondite subject.

military force without actually resorting to war. The

refractory (ri·'frak·to ˘·ree) adj. stubborn, unmanageable,

president promised a swift reprisal for the attack. reprobate ('rep·ro˘·bayt) n. an immoral or unprincipled

resisting control or discipline. Elena is a counselor for refractory children in an alternative school setting.

person; one without scruples. Edgar deemed himself a

regale (ri·'ayl) v. to delight or entertain with a splendid

reprobate, a criminal, and a traitor in his written

feast or pleasant amusement. The king regaled his

confession.

guests until the early morning hours.

repudiate (ri·'pyoo·di·ayt) v. to disown, disavow, reject

remonstrate (ri·'mon·strayt) v. 1. to say or plead in

completely. Ms. Tallon has repeatedly repudiated your accusations.

protest, objection, or opposition 2. to scold or

rescind (ri·'sind) v. to repeal or cancel; to void or annul.

reprove. The children remonstrated loudly when their

They have rescinded their offer, so you must find

babysitter told them they couldn’t watch that movie. renegade ('ren·e˘·ayd) n. 1. a deserter; one who rejects a

another buyer. resonant ('rez·o ˘·na˘nt) adj. echoing, resounding. The new

cause, group, etc. 2. a person who rebels and becomes an outlaw. The renegade soldier decided to join the

announcer at the stadium has a wonderfully resonant

guerilla fighters.

voice. reticent ('ret·i·se˘nt) adj. tending to keep one’s thoughts

renowned (ri·'nownd) adj. famous; widely known and esteemed. The renowned historian Stephen Ambrose

and feelings to oneself; reserved, untalkative, silent.

wrote many books that were popular with both scholars

Annette is very reticent, so don’t expect her to tell you

and the general public.

much about herself. rigmarole ('ri·ma˘·rohl) (also rigamarole) n. 1. rambling,

repartee (rep·a˘r·'tee) n. 1. a quick, witty reply 2. the ability to make witty replies. He wasn’t expecting such a

confusing, incoherent talk 2. a complicated, petty pro-

sharp repartee from someone who was normally so quiet.

cedure. You had to go through a great deal of rigmarole

replete (ri·'pleet) adj. 1. well-stocked or abundantly sup-

to get this approved.

plied 2. full, gorged. The house was replete with expen-

rogue (roh) n. 1. a dishonest, unprincipled person 2. a

sive antiques.

pleasantly mischievous person 3. a vicious and solitary

repose (ri·'pohz) n. 1. resting or being at rest 2. calmness,

animal living apart from the herd. Yesterday, that rogue

tranquility, peace of mind. The wail of a police siren

hid all of my cooking utensils; today he’s switched every-

disturbed my repose.

thing around in the cupboards!

reprehensible (rep·ri·'hen·s˘·be˘l) adj. deserving rebuke

roil (roil) v. 1. to make a liquid cloudy or muddy 2. to stir

or censure. The reprehensible behavior of the neighbor-

up or agitate 3. to anger or annoy. That you could even

hood bully angered everyone on the block.

think such a thing really roils me.

283

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

schism ('skiz·e˘m) n. a separation or division into fac-

rubric ('roo·brik) n. 1. a class or category 2. a heading, title, or note of explanation or direction. I would put

tions because of a difference in belief or opinion. The

this under the rubric of “quackery,” not “alternative

schism between the two parties was forgotten as they

medicine.”

united around a common cause. scintilla (sin·'til·a˘) n. a trace or particle; minute amount,

S

iota. She has not one scintilla of doubt about his guilt. scurvy ('skur·vee) adj. contemptible, mean. That scurvy

sacrilegious (sak·r˘·'lij·u ˘s) adj. disrespectful or irrever-

knave has ruined my plans again. ˘·lu ˘s) adj. diligent, persevering, hard sedulous ('sej·u

ent towards something regarded as sacred. Her book was criticized by the church for being sacrilegious.

working. After years of sedulous research, the

sagacious (sa˘·'ay·shu ˘s) adj. having or showing sound

researchers discovered a cure.

judgment; perceptive, wise. My sagacious uncle always

semantics (si·'man·tiks) n. 1. the study of meaning in

gives me good, sound advice.

language 2. the meaning, connotation, or interpreta-

salient ('say·lee·e˘nt) adj. 1. conspicuous, prominent,

tion of words, symbols, or other forms 3. the study of

highly noticeable; drawing attention through a strik-

relationships between signs or symbols and their

ing quality 2. spring up or jutting out. Jill’s most

meanings. He claims it’s a matter of semantics, but the

salient feature is her stunning auburn hair.

issue is not open to interpretation.

salutary ('sal·yu ˘·ter·ee) adj. producing a beneficial or

sententious (sen·'ten·shu ˘s) adj. 1. expressing oneself

wholesome effect; remedial. To promote better health,

tersely, pithy 2. full of maxims and proverbs offered in

I’ve decided to move to a more salutary climate.

a self-righteous manner. I was looking for your honest

sanctimonious (sank·t˘·'moh·nee·u ˘s) adj. hypocritically

opinion, not a sententious reply. shiftless ('shift·lis) adj. lazy and inefficient; lacking

pious or devout; excessively self-righteous. The thief’s sanctimonious remark that “a fool and his money are soon

ambition, initiative, or purpose. My shiftless roommate

parted” only made the jury more eager to convict him.

has failed all of his classes.

sangfroid (sahn·'frwah) n. composure, especially in dan-

simian ('sim·ee·a˘n) adj. of or like an ape or monkey. Cre-

gerous or difficult circumstances. I wish I had Jane’s

ationists do not believe that humans have simian

sangfroid when I find myself in a confrontational

ancestors.

situation.

sinuous ('sin·yoo·u ˘s) adj. winding, undulating, serpen-

sanguine ('san·win) adj. 1. confidently cheerful, optimistic 2. of the color of blood; red. People are drawn

tine. It is dangerous to drive fast on such a sinuous road. slake (slayk) v. 1. to satisfy, quench 2. to reduce the intensity

to her because of her sanguine and pleasant nature. sardonic (sahr·'don·ik) adj. sarcastic, mocking scorn-

of, moderate, allay. The deer slaked its thirst at the river. sodden ('sod·e˘n) adj. 1. thoroughly saturated, soaked 2.

fully. I was hurt by his sardonic reply.

expressionless or dull, unimaginative. Caught in an

saturnine ('sat·u ˘r·n¯n) adj. gloomy, dark, sullen. The sat-

unexpected rainstorm, I was sodden by the time I

urnine child sulked for hours. savoir faire ('sav·wahr 'fair) n. knowledge of the right

reached the bus stop. solecism ('sol·e˘·siz·e˘m) n. 1. a mistake in the use of lan-

thing to do or say in a social situation; graceful tact.

guage 2. violation of good manners or etiquette,

Savoir faire is essential if you want to be a successful

impropriety. Frank’s solecism caused his debate team

diplomat.

much embarrassment.

284

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

sophistry ('sof·i·stree) n. clever but faulty reasoning; a

Beethoven’s music is simply sublime. subliminal (sub·'lim·˘·na˘l) adj. below the threshold of

plausible but invalid argument intended to deceive by appearing sound. I was amused by his sophistry, but knew

consciousness. Subliminal advertising is devious but

he had a little more research to do before he presented his

effective.

argument to the distinguished scholars in his field.

subvert (sub·'vurt) v. 1. to overthrow 2. to ruin, destroy

sordid ('sor·did) adj. 1. dirty, wretched, squalid 2.

completely 3. to undermine. She quietly subverted his

morally degraded. This sordid establishment should be

authority by sharing internal information with outside

shut down immediately.

agents.

specious ('spee·shu ˘s) adj. 1. seemingly plausible but false

sundry ('sun·dree) adj. various, miscellaneous. The

2. deceptively pleasing in appearance. Vinnie did not

sundry items in her backpack reveal a great deal about

fool me with his specious argument.

her personality.

spurious ('spyoor·ee·u ˘s) adj. false, counterfeit, not gen-

˘s) adj. haughty, scornful, supercilious (soo·pe˘r·'sil·ee·u

uine or authentic. The expert confirmed that the Willie

disdainful. Sunil’s supercilious attitude and sarcastic

Mays autograph was spurious.

remarks annoy me greatly. supplicant ('sup·l˘·ka˘nt) n. a person who asks humbly

squalid ('skwol·id) adj. 1. filthy and wretched 2. morally repulsive, sordid. The housing inspectors noted such

for something; one who beseeches or entreats. The

deplorable and squalid living conditions in the building

supplicants begged for forgiveness. surly ('sur·lee) adj. bad-tempered, gruff, or unfriendly in

on Water Street that they were forced to evacuate the

a way that suggests menace. Emily received a surly

tenants. stoical ('stoh·i·ka ˘l) adj. seemingly unaffected by pleasure or

greeting from the normally cheerful receptionist. surrogate ('sur·o ˘·it) n. a substitute; one who takes the

pain; indifferent, impassive. He remained stoical while

place of another. Martha agreed to be a surrogate

his wife told him she was leaving.

mother for her sister.

stolid ('stohl·id) adj. not feeling or showing emotion,

svelte (svelt) adj. slender and graceful, suave. The svelte

impassive; not easily aroused or excited. Maxine is a

actress offered a toast to her guests.

very stolid person, so it will be difficult to tell how she

sycophant ('sik·o ˘·fa˘nt) n. a person who tries to win the

feels. stringent ('str¯·de˘nt) adj. very strict, according to very

favor of influential or powerful people through flat-

rigorous rules, requirements or standards. The strin-

tery; a fawning parasite. The president is surrounded by

gent eligibility requirements greatly limited the number

sycophants, so how will he really know if his ideas have

of candidates for the scholarship.

merit?

stultify ('stul·t˘·f¯) v. 1. to impair or make ineffective, cripple 2. to make (someone) look foolish or incom-

T

petent. Of course I’m angry! You stultified me at that meeting!

taciturn ('tas·i·turn) adj. habitually untalkative, reserved.

stymie ('st¯·mee) v. to hinder, obstruct, thwart; to pre-

I’ve always known him to be taciturn, but yesterday he

vent the accomplishment of something. The negotia-

regaled me with tales of his hiking adventures. tangible ('tan·j˘·be˘l) adj. able to be perceived by touch,

tions were stymied by yet another attack. sublime (su ˘·'bl¯m) adj. having noble or majestic qualities; inspiring awe, adoration, or reverence; lofty, supreme.

285

palpable; real or concrete. There is no tangible evidence of misconduct; it’s all hearsay.

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

tawdry ('taw·dree) adj. gaudy or showy but without any

The totalitarian regime fell quickly when the people

real value; flashy and tasteless. I’ve never seen such a

revolted. tractable ('trak·ta˘·be˘l) adj. easily managed or controlled;

tawdry outfit as the three-tiered taffeta gown that the music singer wore to the awards ceremony!

obedient, docile. In the novel Brave New World, the

teem (teem) v. to be full of; to be present in large num-

World Controllers use hypnosis and a “happiness drug”

bers. This city is teeming with tourists during the sum-

to make everyone tractable. transient ('tran·zhe˘nt) adj. lasting only a very short

mer months. temerity (te˘·'mer·i·tee) n. foolish disregard of danger;

time; fleeting, transitory, brief. Their relationship was

brashness, audacity. This is no time for temerity; you

transient but profound. trenchant ('tren·cha˘nt) adj. 1. penetrating, forceful,

must move cautiously to avoid any further damage. tenacious (te˘·'nay·shu ˘s) adj. 1. holding firmly to some-

effective 2. extremely perceptive, incisive 3. clear-cut,

thing, such as a right or principle; persistent, stub-

sharply defined. It was a trenchant argument, and it

bornly unyielding 2. holding firmly, cohesive 3.

forced me to change my mind about the issue.

sticking firmly, adhesive 4. (of memory) retentive.

tribunal (tr¯·'byoo·na˘l) n. a court of justice. He will be

When it comes to fighting for equality, she is the most

sentenced for his war crimes by an international

tenacious person I know.

tribunal.

tendentious (ten·'den·shu ˘s) adj. biased, not impartial,

truculent ('truk·yu ˘·le˘nt) adj. 1. defiantly aggressive 2.

partisan; supporting a particular cause or position.

fierce, violent 3. bitterly expressing opposition. The

The tendentious proposal caused an uproar on the Sen-

outspoken council president gave a truculent speech

ate floor.

arguing against the proposal.

tenet ('ten·it) n. a belief, opinion, doctrine or principle

truncate ('trun·kayt) v. to shorten or terminate by (or

held to be true by a person, group, or organization.

as if by) cutting the top or end off. The glitch in the

This pamphlet describes the tenets of Amnesty

software program truncated the lines of a very impor-

International.

tant document I was typing.

tenuous ('ten·yoo·u ˘s) adj. 1. unsubstantial, flimsy 2. hav-

tumultuous (too·'mul·choo·u ˘s) adj. 1. creating an

ing little substance or validity. Though the connection

uproar, disorderly, noisy 2. a state of confusion, tur-

between the two crimes seemed tenuous at first, a thor-

bulence, or agitation, tumult. It was another tumul-

ough investigation showed they were committed by the

tuous day for the stock market, and fluctuating prices

same person.

were wreaking havoc for investors.

timorous ('tim·o ˘·ru ˘s) adj. fearful, timid, afraid. The stray

turpitude ('tur·pi·tood) n. 1. wickedness 2. a corrupt or

dog was timorous, and it took a great deal of coaxing to

depraved act. Such turpitude deserves the most severe

get him to come near the car.

punishment.

toil (toil) n. exhausting labor or effort; difficult or laborious work. v. to work laboriously, labor strenuously.

U

Evan toiled for hours before solving the problem. totalitarian (toh·'tal·i·'tair·ee·a˘n) adj. of a form of gov-

umbrage ('um·brij) n. offense, resentment. I took great

ernment in which those in control neither recognize

umbrage at your suggestion that I twisted the truth.

nor tolerate rival parties or loyalties, demanding total

undulate ('un·ju ˘·layt) v. to move in waves or in a wavelike

submission of the individual to the needs of the state.

fashion, fluctuate. The curtains undulated in the breeze.

286

–APPENDIX 4: COMMONLY TESTED VOCABULARY WORDS–

untoward (un·'tohrd) adj. 1. contrary to one’s best inter-

vex (veks) v. 1. to annoy, irritate 2. to cause worry to. I

est or welfare; inconvenient, troublesome, adverse 2.

was completely vexed by his puerile behavior.

improper, unseemly, perverse. Jackson’s untoward

vitriolic (vit·ri·'ol·ik) adj. savagely hostile or bitter, caus-

remarks made Amelia very uncomfortable.

tic. Her vitriolic attack on her opponent was so hostile

upbraid (up·'brayd) v. to reprove, reproach sharply, con-

that it may cost her the election. volatile ('vol·a˘·til) adj. 1. varying widely, inconstant,

demn; admonish. The child was upbraided for misbehaving during the ceremony.

changeable, fickle 2. unstable, explosive, likely to

urbane (ur·'bayn) adj. elegant, highly refined in man-

change suddenly or violently 3. (in chemistry) evapo-

ners, extremely tactful and polite. Christopher thinks

rating readily. Dan’s volatile personality has been com-

he’s so urbane, but he’s really quite pedestrian.

pared to that of Dr. Jekyll and Mr. Hyde. voluble ('vol·yu ˘·be˘l) adj. 1. talking a great deal and with

V

great ease; language marked by great fluency; rapid, nimble speech 2. turning or rotating easily on an axis.

vacuous ('vak·yoo·u ˘s) adj. empty, purposeless; senseless,

Your new spokesperson is very voluble and clearly com-

stupid, inane. This TV show is yet another vacuous

fortable speaking in front of large audiences. voracious (voh·'ray·shu ˘s) adj. excessively greedy, rapa-

sitcom. venal ('vee·na˘l) adj. easily bribed or corrupted; unprinci-

cious; having a great appetite for something, devour-

pled. The venal judge was removed and disbarred.

ing greedily. I have always been a voracious reader and

venerable ('ven·e˘·ra˘·be˘l) adj. worthy of reverence or

consume dozens of books every month.

respect because of age, dignity, character or posiX

tion. The venerable Jimmy Carter won the Nobel Peace Prize. verbose (ve˘r·'bohs) adj. using more words than neces-

xenophobia (zen·o ˘·'foh·bee·a˘) n. a strong dislike, dis-

sary; wordy, long-winded. Her verbose letter rambled

trust, or fear of foreigners. Many atrocities have been

so much that it didn’t seem to have a point.

committed because of xenophobia.

verisimilitude (ver·'i·si·'mil·i·tood) n. the appearance of being true or real. The movie aims for complete

Z

verisimilitude and has painstakingly recreated the details of everyday life in the 1920s.

zenith ('zee·nith) n. 1. the highest point, top, peak 2. the

veritable ('ver·i·ta˘·be˘l) adj. real, true, genuine. Einstein

point in the sky directly above the observer. She is at

was a veritable genius.

the zenith of her career and has won every case this year.

287

Appendix 5: Prefixes, Suffixes, and Word Roots 

Prefixes

Prefixes are syllables added to the beginnings of words to change or add to their meaning. This table lists some of the most common prefixes in the English language. They are grouped together by similar meanings. PREFIX

MEANING

EXAMPLE

DEFINITION

SENTENCE

uni-

one

unify v.

to form into a

The new leader was able to

single unit, to unite

unify the three factions into one strong political party.

mono-

bi-

duo-

one

two

two

monologue n.

bisect v.

duality n.

a long speech by one

I was very moved by the

person or performer

monologue in Scene III.

to divide into two

If you bisect a square, you will

equal parts

get two rectangles of equal size.

having two sides or parts

The novel explores the duality of good and evil in humans.

tri-

three

triangle n.

a figure having three

In an isosceles triangle, two

angles

of the three angles are the same size.

quadri-

four

quadruped n.

an animal with four feet

Some quadrupeds evolved into bipeds.

289

–APPENDIX 5: PREFIXES, SUFFIXES, AND WORD ROOTS–

PREFIX

MEANING

EXAMPLE

DEFINITION

SENTENCE

tetra-

four

tetralogy n.

series of four related

“Time Zone” was the

artistic works

fourth and final work in Classman’s tetralogy.

quint-

pent-

multi-

five

five

many

quintuplets n.

pentameter n.

multifaceted adj.

five offspring born at

Each quintuplet weighed

one time

less than four pounds at birth.

a line of verse (poetry)

Most of Shakespeare’s sonnets

with five metrical feet

are written in iambic pentameter.

having many sides

This is a multifaceted issue, and you must examine each side carefully.

poly-

omni-

many

all

polyglot n.

omniscient adj.

one who speaks or

It’s no wonder she’s a polyglot;

understands several

she’s lived in eight different

language

countries.

knowing all

Dr. Perez seems omniscient; she knows what all of us are thinking in class.

micro-

small

microcosm n.

little or miniature world;

Some people say that Brooklyn

something representing

Heights, the Brooklyn district

something else on a very

across the river from the Wall

small scale

Street area, is a microcosm of Manhattan.

mini-

small

minority n.

small group within a

John voted for Bridget, but he

larger group

was in the minority; most people voted for Elaine.

macro-

large

macrocosm n.

the large scale world or

Any change to the macrocosm

universe; any great whole

will eventually effect the microcosm.

ante-

before

anticipate v.

to give advance thought; to

His decades of experience

foresee; expect

enabled him to anticipate the problem.

pre-

post-

before

after

precede v.

postscript n.

to come before in time

The appetizers preceded the

or order

main course.

message added after the

His postscript was almost as

close of a letter

long as his letter!

290

–APPENDIX 5: PREFIXES, SUFFIXES, AND WORD ROOTS–

PREFIX

MEANING

EXAMPLE

DEFINITION

SENTENCE

inter-

between

intervene v.

to come between

Romeo, trying to make peace, intervened in the fight between Tybalt and Mercutio.

inter-

together

interact v.

to act upon or influence each other

The psychologist took notes as she watched the children interact.

intra-

within

intravenous adj.

within or into a vein

She couldn’t eat and had to be fed intravenously for three days.

intro-

into, within

introvert n.

a person whose attention

Unlike his flamboyant sister,

is largely directed inward,

quiet Zeke was a real introvert.

toward himself or herself; a shy or withdrawn person in-

in, into

induct v.

to bring in (to a group)

She was inducted into the honor society.

ex-

out, from

expel v.

to drive out or away

Let’s expel the invaders!

circum-

around

circumscribe v.

to draw a line around;

She carefully circumscribed

to mark the limits of

the space that would become her office.

sub-

under

subvert v.

to bring about the

His attempt to subvert my

destruction of, overthrow;

authority will cost him his job.

to undermine super-

above, over

supervisor n.

one who watches over

Alex refused the promotion to supervisor because he didn’t feel comfortable being his friends’ boss.

con-

with, together

consensus n.

general agreement

After hours of debate, the group finally reached a consensus and selected a candidate.

non-

not

nonviable adj.

not able to live or survive

The farmer explained that the seedling was nonviable.

in-

not

invariable adj.

not changing

The weather here is invariable— always sunny and warm.

un-

not, against

unmindful adj.

not conscious or aware

For better or worse, he is

of; forgetful

unmindful of office politics.

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PREFIX

MEANING

EXAMPLE

DEFINITION

SENTENCE

contra-

against

contradict v.

to state that (what is said)

I know we don’t have to agree

is untrue; to state the

on everything, but she

opposite of

contradicts everything I say.

antipode n.

exact or direct opposite

North is the antipode of south.

against,

counter-

working against

Complaining is

opposing

productive adj.

production

counterproductive.

away,

dispel v.

to drive away

anti-

against, opposite

counter-

dis-

To dispel rumors that I was quitting, I scheduled a series of meetings for the next three months.

dis-

mis-

not,

wrong, ill

opposite of

not having order; messy,

Two people were hurt when the

disorderly adj.

untidy, uncontrolled

crowd became disorderly during

or unruly

the protest.

to use wrongly

She misused her authority

misuse v.

when she reassigned Charlie to a new team. mal-

bad, wrong,

maltreat v.

to treat badly or wrongly

After the dog saved his life, he swore he would never maltreat another animal.

mal-

ill

malaise n.

feeling of discomfort

The malaise many women

or illness

feel during the first few months of pregnancy is called “morning sickness.”

pseudo-

false, fake

pseudonym n.

false or fake name

Mark Twain is a pseudonym for Samuel Clemens.

auto-

by oneself

automaton n.

or by itself

co-

together with; jointly

cohesive adj.

a robot; a person who

The workers on the

seems to act mechanically

assembly line looked like

and without thinking

automatons.

having a tendency to bond

Though they came from

or stick together; united

different backgrounds, they have formed a remarkably cohesive team.

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–APPENDIX 5: PREFIXES, SUFFIXES, AND WORD ROOTS–



Suffixes

Suffixes are syllables added to the ends of words to change or add to their meaning. This table lists some of the most common suffixes in the English language. They are grouped together by similar meanings. SUFFIX

MEANING

EXAMPLE

DEFINITION

SENTENCE

-en

to cause

broaden v.

to make more broad,

Traveling around the world will

widen

broaden your understanding of

to become

other cultures. -ate

to cause to be resuscitate v.

to bring or come back

Thanks to a generous gift

to life or consciousness;

from an alumnus, we were

to revive

able to resuscitate the study-abroad program.

-ify/-fy

to make or

electrify v.

to charge with electricity

cause to be -ize

to make,

alphabetize v.

to put in alphabetical order

to give -al

capable of,

The singer electrified the audience with her performance. Please alphabetize these files for me.

practical adj.

suitable for

suitable for use; involving

He has years of practical,

activity, as distinct from

on-the-job experience.

study or theory -ial

pertaining to

commercial adj.

of or engaged in commerce

Commercial vehicles must have special license plates.

-ic

pertaining to

aristocratic adj.

of or pertaining to

Though he was never rich

the aristocracy

or powerful, he has very aristocratic manners.

-ly

resembling,

tenderly adv.

having the

done with tenderness;

He held the newborn baby

gently, delicately, lovingly

tenderly in his arms.

in a bold manner

Despite his fear, he stepped

qualities of -ly

in the manner

boldly adv.

of -ful

full of

boldly onto the stage. meaningful adj.

significant, full of meaning

When Robert walked into the room with Annette, she cast me a meaningful glance.

-ous, -ose

full of

humorous adj.

full of humor, funny

His humorous speech made the evening go by quickly.

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SUFFIX

MEANING

EXAMPLE

DEFINITION

SENTENCE

-ive

having the

descriptive adj.

giving a description

The letter was so descriptive

quality of

that I could picture every place he’d been.

-less

-ish

lacking, free of painless adj.

having the

childish adj.

quality of

without pain,

The doctor assured me that it is

not causing pain

a painless procedure.

like a child; unsuitable for

He didn’t get the job because

a grown person

of his childish behavior during the interview.

-ance/

quality or

-ence

state of

-acy

quality or

tolerance n.

indeterminacy n.

state of

-tion

act, state or

completion n.

condition of

willingness or ability

He has a high level of

to tolerate a person or thing

tolerance for rudeness.

state or quality of being

The indeterminacy of his

undetermined (without

statement made it impossible

defined limits) or vague

to tell which side he was on.

the act of completing;

The second siren signaled

the state of being

the completion of the fire drill.

completed or finished -or/-er

one who does

narrator n.

or performs

one who tells the story,

A first-person narrator

gives an account of

is usually not objective.

the action of -atrium

place for

arboretum n.

-orium

a garden devoted primarily

They built a deck with an

to trees and shrubs

arboretum for their bonsai tree

-etum -ary

collection. place for,

sanctuary n.

a sacred place, refuge

pertaining to

With three noisy roommates, Ellen frequently sought the quiet sanctuary of the library.

-cide

kill

pesticide n.

substance for killing insects This pesticide is also dangerous for humans.

-ism

belief that things will

Her optimism makes people

or condition of;

quality, state

optimism n.

turn out for the best;

want to be around her.

doctrine of

tendency to take a hopeful view of things

-ity

quality or state of

morality n.

state or quality of

He argued that the basic

being moral

morality of civilized societies hasn’t changed much over the centuries.

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–APPENDIX 5: PREFIXES, SUFFIXES, AND WORD ROOTS–

SUFFIX

MEANING

EXAMPLE

DEFINITION

SENTENCE

-itis

inflammation of

tonsillitis n.

inflammation and

Her tonsillitis was so severe that

infection of the tonsils

doctors had to remove her tonsils immediately.

-ment

act or

judgment n.

condition of

-ology

the study of

zoology n.

ability to judge or make

He exercised good

decisions wisely; act

judgment by keeping his

of judging

mouth shut during the meeting.

the scientific study of

She took a summer job at the

animal life

zoo because of her strong interest in zoology.



Common Latin Word Roots

Many words in the English language have their origins in Latin. The following table shows the original Latin words that you have used (whether you know it or not) to create various English words. The Latin words serve as roots, providing the core meaning of the words; prefixes, suffixes, and other alterations give each word its distinct meaning. The word roots are listed in alphabetical order. ROOT

MEANING

EXAMPLE

DEFINITION

SENTENCE

amare

to love

amorous adj.

readily showing or

She told him to stop his

feeling love

amorous advances, as she was already engaged.

audire

bellum

to hear

war

audience n.

belligerent adj.

assembled group of

The audience was stunned

listeners or spectators;

when the game show host

people within hearing

slapped the contestant.

inclined to fight; hostile,

The citizens feared that

aggressive

their belligerent leader would start an unjust war.

capere

to take

captivate v.

to capture the fancy of

The story captivated me from the beginning; I couldn’t put the book down.

dicere

to say, speak

dictate v.

to state or order; to say what She began to dictate her needs to be written down

295

notes into the microphone.

–APPENDIX 5: PREFIXES, SUFFIXES, AND WORD ROOTS––

ROOT

MEANING

EXAMPLE

DEFINITION

SENTENCE

duco

to lead

conduct v.

to lead or guide (thorough)

He conducted a detailed tour of the building.

equus

equal

equilibrium n.

a state of balance

I have finally achieved an equilibrium between work and leisure.

facere

to make or do

manufacture v.

to make or produce

The clothes are manufactured here in this factory.

lucere

to light

lucid adj.

very clear

No one could possibly have misunderstood such a lucid explanation.

manus

medius

hand

middle

manicure n.

median adj.

cosmetic treatment of

To maintain her long fingernails,

the fingernails

she gets a manicure every week.

middle point; middle in

The median household income

a set of numbers

in this wealthy neighborhood is $89,000.

mittere

to send

transmit v.

to send across

The message was transmitted over the intercom.

omnis

all, every

omnipresent adj.

present everywhere

That top-40 song is omnipresent; everywhere I go, I hear it playing.

plicare

ponere/

to fold

to place

application n.

position n.

positum

putting one thing on

His loan application was

another; making a formal

denied because of his poor

request

credit history.

the place a person or

Although he is only 22,

thing occupies

he holds a very powerful position in the company.

protare

to carry

transport v.

to carry across

The goods will be transported by boat.

quarere

to ask,

inquiry n.

question

act of inquiry, investigation,

The inquiry lasted several

or questioning

months but yielded no new information.

scribere

to write

scribe n.

person who makes

The scribe had developed thick

copies of writings

calluses on his fingers from years of writing.

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–APPENDIX 5: PREFIXES, SUFFIXES, AND WORD ROOTS–

ROOT

MEANING

EXAMPLE

DEFINITION

SENTENCE

sentire

to feel

sentient adj.

capable of feeling

No sentient beings should be used for medical research.

specere

to look at

spectacle n.

striking or impressive sight

The debate was quite a spectacle—you should have seen the candidates attack one another.

spirare

to breathe

respiration n.

the act of breathing

His respiration was steady, but he remained unconscious.

tendere

to stretch

extend v.

to make longer, stretch out

Please extend the deadline by two weeks so you can complete the project properly.

verbum

word

verbatim adv.

word for word

The student failed because she had copied an article verbatim instead of writing her own essay.



Common Greek Word Roots

Many other English words have their origins in the ancient Greek language. The following table shows the Greek words that you have used (whether you know it or not) to create various English words. The Greek words serve as roots, providing the core meaning of the words; prefixes, suffixes, and other alterations give each word its distinct meaning. The word roots are listed in alphabetical order. ROOT

MEANING

EXAMPLE

DEFINITION

SENTENCE

bios

life

biology n.

the science of

He is majoring in biology and

living organisms

plans to go to medical school.

arranged in the order in

The story is confusing because

which things occurred

she did not put the events in

chronos

time

chronological adj.

chronological order. derma

gamos

skin

marriage, union

dermatology n.

polygamy n.

branch of medical science

She has decided to study

dealing with the skin and

dermatology because she has

its diseases

always been plagued by rashes.

the practice or custom of

Throughout history, certain

having more than one

cultures have practiced

spouse or mate at a time

polygamy, but it is uncommon today.

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–APPENDIX 5: PREFIXES, SUFFIXES, AND WORD ROOTS–

ROOT

MEANING

EXAMPLE

genos

race, sex, kind genocide n.

DEFINITION

SENTENCE

deliberate extermination

The recent genocide in Bosnia

of one race of people

has created a crisis in orphaned children.

geo

earth

geography n.

the study of the Earth’s

The geography of this region

surface; the surface or

made it difficult for the different

topographical features of

tribes to interact

a place. graphein

to write

calligraphy n.

beautiful or elegant

She used calligraphy when she

handwriting

addressed the wedding invitations.

krates

member of

democrat n.

a group

kryptos

hidden, secret cryptic adj.

one who believes in or

I have always been a

advocates democracy as

democrat, but I refuse to join

a principle of government

the democratic party.

concealing meaning,

He left such a cryptic message

puzzling

on my answering machine that I don’t know what he wanted.

metron

morphe

to measure

form

metronome n.

polymorphous adj.

device with a pendulum that

She used a metronome to help

beats at a determined rate

her keep the proper pace as she

to measure time/rhythm

played the song.

having many forms

Most mythologies have a polymorphous figure, a “shape shifter,” who can be both animal and human.

pathos

suffering,

pathetic adj.

arousing feelings of pity

feeling

Willy Loman is a complex or sadness

character who is both pathetic and heroic.

philos

loving

xenophile n.

a person who is attracted

Alex is a xenophile; I doubt he’ll

to foreign peoples,

ever come back to the States.

cultures or customs phobos

fear

xenophobe n.

person who fears or hates

Don’t expect Len to go on the

foreigners or strange

trip; he’s a xenophobe.

cultures, or customs photos

light

photobiotic adj.

living or thriving only in

Plants are photobiotic and will

the presence of light

die without light.

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–APPENDIX 5: PREFIXES, SUFFIXES, AND WORD ROOTS–

ROOT

MEANING

EXAMPLE

DEFINITION

SENTENCE

podos

foot

podiatrist n.

an expert in diagnosis

The podiatrist saw that the

and treatment of ailments

ingrown toenail had

of the human foot

become infected.

false name

Was George Eliot a pseudonym

psuedein

to deceive

pseudonym n.

for Mary Ann Evans? pyr

fire

pyromaniac n.

one who has a compulsion

The warehouse fire was not an

to set things on fire

accident; it was set by a pyromaniac.

soma

body

psychosomatic adj. of or involving both the mind and body

In a psychosomatic illness, physical symptoms are caused by emotional distress.

tele

distant

telescope n.

optical instrument for

While Galileo did not invent the

making distant objects

telescope, he was the first to

appear larger and nearer

use it to study the planets and

when viewed through the

stars.

lens therme

heat

thermos n.

insulated jug or bottle that

The thermos kept my coffee hot

keeps liquids hot or cold

all afternoon.

299